Logic Challenge #18 - Rock and Ball

[stampytherhino]

I think I got it:

1 A
2 E
3 D
4 D
5 C
6 B
7 C

[foofighter20x]

1. A
2. E
3. D
4. B
5. C
6. B
7. C

Maybe a few wrong answers in there... :p

[hartlogan]

I sent an email, but I figure I'll post here as well.

1) A
2) E
3) D
4) E
5) C
6) B - answered A in the email, but re-assessed to B
7) C

[edeiber]

1. A
2. E
3. D
4. E
5. C
6. B
7. C

Is what I emailed in when I did it earlier. Looks like we're all in suspense on the answer for the one question.

[foofighter20x]

I'm actually thinking 4 is E now, but there's a real problem with that question. Explanations to follow will show why.

[jessika.thomas]

Explanations:

Q1:
1. Which one of the following could be a correct assignment of players to starting positions?

(A) Guards: Ronnie Spector and Stevie Nicks; Forwards: Michael Stipe and Prince; Center: Ozzy Osbourne
CORRECT
(B) Guards: Ronnie Spector and Stevie Nicks; Forwards: Michael Stipe and Tina Turner; Center: Prince
M and T cannot be forwards together, since the positions must be filled by two men or two women
(C) Guards: Prince and Neil Young; Forwards: Ronnie Spector and Stevie Nicks; Center: Tina Turner
T cannot be the Center since O is not a Guard
(D) Guards: Ozzy Osbourne and Prince; Forwards: Michael Stipe and Neil Young; Center: Tina Turner
N cannot be a Forward
(E) Guards: Ronnie Spector and Ozzy Osbourne; Forwards: Michael Stipe and Prince; Center: Tina Turner
R and O cannot be guards together, since the positions must be filled by two men or two women

Q2:
2. If Stevie Nicks starts at forward, which one of the following must be false?

If S is forward, the other forward must be T or R. Both guards must be male (since there are only 3 women and forwards & guards must be the same sex as the other in that position).

(A) Tina Turner starts at forward.
could be true
(B) Ronnie Spector starts at forward.
could be true
(C) Ozzy Osbourne starts at center.
could be true
(D) Neil Young starts at center.
could be true
(E) Ronnie Spector starts at guard.
Correct answer--must be false because the guards must be male

Q3:
3. Which one of the following pairs of assignments would determine the assignment of the remaining positions?

The easiest way to start with a question like this is to look at the most restrictive possibility. Thus, I would start with T as center (since we know that O must then be a guard).

If the forward is a male, then we can assign all positions quickly.
(A) Guard: Michael Stipe; Forward: Ronnie Spector
(B) Guard: Neil Young; Forward: Stevie Nicks
(C) Guard: Neil Young; Center: Tina Turner
(D) Forward: Michael Stipe; Center: Tina Turner
If T is Center, O must be a guard. Since M is forward, the other forward must be male. Since N cannot be a forward, he must be the second guard. Thus P must be the second forward.
(E) Forward: Michael Stipe; Forward: Prince

Q4:
4. Which one of the following, if substituted for the restriction that if Tina Turner starts at center, Ozzy Osbourne starts at guard, would have the same effect on determining who will start?

(A) If Ozzy Osbourne starts at center, Tina Turner will not start at center.
Duh? This rule means nothing since there is only one center.
(B) If a woman starts at guard, Tina Turner will not start at center.
This is true with the rule as stated previously, since the guards must be men if T starts, but it does not specify that O must be one of the guards if T starts at center.
(C) If a woman starts at guard, Ozzy Osbourne will not start at guard.
Well yes, given rule 1, but this fails to link T as C with O as guard.
(D) If Ozzy Osbourne does not start at guard, a woman will not start at center.
Correct: T is the only women who can start at center. Thus, O must start at guard if T is center has the same impact of saying that a woman can only start center if he is guard. Note that neither rule prohibits O from being guard even if T does not start center.
(E) If a woman starts at center, Neil Young will start at guard.
This does result in T (the only possible female center) having male guards, but it does not restict the other guard to being O.

Q5:
5. Which one of the following could be true?

(A) Four men and one woman start, and Neil Young starts at center.
Cannot have one woman as either one of the guards or one of the forwards--both guards and forwards must be both male or both female, since the center is identified as male, this must be false.
(B) Three men and two women start, and Tina Turner starts at center.
Cannot have one woman as either one of the guards or one of the forwards--both guards and forwards must be both male or both female, since the center is identified as female, this must be false--there would still be one female as a mismatched guard or forward.
(C) Three men and two women start, and Tina Turner starts at guard.
Correct answer--T and R or S may be guard, forwards must be M and P (since O and N cannot be forwards), and the center can be either O or N.
(D) Two men and three women start, and Tina Turner starts at guard.
If there are three women, two must be the fowards and the other must be the center. Since only T can be center (and O and one other man must then be the guards), this must be false.
(E) Two men and three women start, and Michael Stipe starts at forward.
If there are three women, two must be the fowards and the other must be the center. Only T can be center, and O must then be a guards. R and S must be the fowards, and the other guard must be male. Since the forwards must be female, M cannot be a forward, and this must be false.

Q6:
If Ronnie Spector starts at guard, how many different starting line-ups are possible?

If R starts as a guard, S or T must be a guard to maintain rule 1.
No woman can be center, because S cannot be and if T is center O must be a guard, which he can't because both guards must be women.
The forwards must be M and P, because they must be men (not enough women for women to be both guards and forwards) and rule 4 says that O and N can not be forwards.
Thus, only O and N can be centers.

Options are: (in order center, G2, G1, F1, F2)
O, S, R, M, P
O, T, R, M, P
N, S, R, M, P
N, T, R, M, P


The correct answer is B, 4.

Q7:
If the tournament decides to change the rules and require the team to add a sixth starter"”a second center who must be female"”and all the other rules remain in effect, which one of the following must be false?

If a 6th player, a woman, starts at center, that player must be T since she is the only woman able to start center.
Thus, O must be a guard.
The other center must be a male since niether R or S can be a center.
Since five positions cannot be filled by 4 men, R and S must the the forwards.
This leaves M, N, and P to fill the remaining two positions: one guard and one center. There are not further restrictions on which player is assigned to these positions.

A--N could start, true.
B--S must start, true.
C--M and P cannot start the same position type--they could both start, but one would be guard and one center, FALSE, so C is the correct answer
D--R and S are both forwards, true
E--O and P could be at the same or different positions--could be true or false, but does not have to be false.

[lrthompson]

Answers:
1)
*a - yes, could happen
b - no, forwards don't match (Male/Male)
c - no, Tina Turner is at Center and Ozzie isn't a Guard
d - no, Neil isn't allowed to be a Forward
e - no, Guards don"t match (Femal/Female)
2)
a - no, could happen
b - no, could happen
c - no, could happen
d - no, could happen
*e - YES, cannot happen - Guards and Forwards must have matching sexes. There are only 3 women and 4 positions to fill if both Forwards and Guards are to be women.
3)
a - no, more than one possibility
b - no, more than one possibility
c - no, more than one possibility
*d - yes, With T as a Center, This dictates O be a Guard, and With M as a Forward, P must also be a forward (since N, amd O cannot be). This leaves only N to be the other Guard. Making the arrangement Guards: O, N. Forwards: M, P. Center: T
e - no, more than one possibility

4) - the rule DEFINES one extra position for us upon knowing one position.
a - no, leaves many possibilities
b - no, leaves many possibilites at center position
c - no, only eliminates a few possibilities of combinations
d - no, leaves a few possibilites
*e - yes, upon knowing that a woman (not R or S... aka T) starts at Center, the rule defines one other position for us.
5)
a - no, Forward and Guard pairs need to match in sex.
b - no, again, Forward and Guard pairs need to match in sex
*c - yes, this allows the Forwards and Guards to match in sex, and a male can be at Center (since it is not Tina)
d - no, If 3 women start, Tina needs to be at Center, since R and S can't be
e - No, If there are 3 women, Tina needs to be at center, making the Guards men (Ozzie is male), so Michael can not start at Forward.

6) If R starts at Guard, the starting arrangement looks like this:
Guards: R, (S/T). Forwards: M, P. Center: (N/O) - This is because the sexes must match, and N and O are not allowed to be Forwards.
With 2 positions and 2 variables in each, that makes 4 combinations.
*The answer is b

7)With all other conditions the same, this means the extra Center must be Tina. Which in turn means that Ozzie is a Guard. This makes R and S Forwards.
The starting arrangement looks like this:
Guards: O, (M/N/P). Forwards: R, S. Centers: (M/N/P), T

a - no, could happen.
b - no, must happen
*c - yes, M and P can not have the same starting title
d - no, must happen
e - no, could happen

[foofighter20x]

1.

A. Correct answer.
B. Breaks rule 2 (R2)
C. Breaks R5
D. Breaks R4
E. Breaks R1

2.

A. Could be true.
B. Could be true.
C. Could be true.
D. Could be true.
E. Must be false. Only three women. Both of each position must be same sex. One runs out of women players in this choice.

3.

A. No clues to who is other guard, who is other forward, nor who is center.
B. Same as A.
C. If Tina is center, then Ozzy is guard. Neil also guard. Who are forwards?
D. Correct. If Tina center, the Ozzy guard. If Mike forward, then another male forward. Only other possible male forward is Prince. If Ozzy guard, then another male guard. Leaves only Neil Young to be guard.
E. No indication as to who is center and who are guards.

4. VERY VERY tricky question.

A. Truism. Doesn't connect center-to-guard aspect of rule.
B. Almost correct. Rule: If Tina center, the Ozzy guard. Contrapositive: If Ozzy not guard, then Tina not center. Equivalency to "Ozzy not guard": If a woman starts as guard, then both guards are women (R1). Thus, Ozzy cannot be a guard. Thus, Tina not center.
C. Same as A.
D. Also almost correct. If Ozzy not guard, then Tina not center. Combine that with R3, and you get If Ozzy not guard, then no women can be center.
E. This is the answer. If a woman is center (only Tina can be a woman center), then Neil Young is guard. R5 leaves open all males to other guard position. This rule does the same. If forwards are female, all males can play position. If forwards are male, they must be M and P, which leaves only O and N for guards. Has the exact same effect as other rule.

5.

A. Violates R1 and R2
B. Same.
C. This works. Tina and another woman as guards, M and P as forwards, and either O or N as center.
D. Violates R3. If Tina is guard, then another woman must be center for it to work, but only Tina can be a woman center.
E. Violates R5. M as forward requires P as forward (R2 and R4). Three women requires Tina be center (R3), but that in turn requires Ozzy be guard (R5).

6. If R is a guard, S or T can be a guard; S cannot be center (R3), T cannot be center (R5). Only M and P can be forwards (R4). Leaves O and N for center. Two combos as guards times two combos as centers equal 4 combos.

R, T, M, P, O/N
R, S, M, P, O/N

B.

7. Only Tina can be female center. Makes Ozzy guard. Leave 3 males to cover 4 positions; thus, only females (R and S) can be forwards, which leaves one guard spot and one center spot. This requires that M and P cannot start the same position.

A. N can start
B. S must start.
C. Must be false.
D. R and S are both forwards.
E. O is a guard, and P could be a guard or a center, so this could be true.

[rippinradio]

4) - the rule DEFINES one extra position for us upon knowing one position.
a - no, leaves many possibilities
b - no, leaves many possibilites at center position
c - no, only eliminates a few possibilities of combinations
d - no, leaves a few possibilites
*e - yes, upon knowing that a woman (not R or S... aka T) starts at Center, the rule defines one other position for us.

We need the rule to do more than define another starting position; we need it to force O into one of the guard slots whenever T occupies the center slot. E doesn't do this. D, on the other hand, is essentially the contrapositive of the fifth rule in disguise. Take the contrapositive of D:
if woman at center (has to be T due to the third rule), then Ozzy at guard

4. VERY VERY tricky question.

A. Truism. Doesn't connect center-to-guard aspect of rule.
B. Almost correct. Rule: If Tina center, the Ozzy guard. Contrapositive: If Ozzy not guard, then Tina not center. Equivalency to "Ozzy not guard": If a woman starts as guard, then both guards are women (R1). Thus, Ozzy cannot be a guard. Thus, Tina not center.
C. Same as A.
D. Also almost correct. If Ozzy not guard, then Tina not center. Combine that with R3, and you get If Ozzy not guard, then no women can be center.
E. This is the answer. If a woman is center (only Tina can be a woman center), then Neil Young is guard. R5 leaves open all males to other guard position. This rule does the same. If forwards are female, all males can play position. If forwards are male, they must be M and P, which leaves only O and N for guards. Has the exact same effect as other rule.

Again, E doesn't ensure that O fills one of the guard slots whenever T starts at center. It does so when the forwards are males, but not when they are females.

[stampytherhino]

WRT Question #4:

4. Which one of the following, if substituted for the restriction that if Tina Turner starts at center, Ozzy Osbourne starts at guard, would have the same effect on determining who will start?

A way to interpret the question is that our goal is to find a rule equivalent to rule 5. I think it's pretty easily answered if you originally outlined the contrapositive of the one that's ousted:

T(c) --> O(g)
not O(g) --> not T(c)

Keep in mind rule 3, which forbids R and S to be center -- and thus the only woman who can be center is Tina Turner (and rightfully so! It's a tough position to fill, and only Tina's tough enough to do it right).

Again, we want a rule that will have the same effect as the previous rule -- in short, intuition suggests we might want to find something pretty close to the contrapositive. D says:

not O(g) --> not R(c) and not S(c) and not T(c)

Combining that with rule 3 means that choice D) *is* the contrapositive we were looking for.

The others:

A) says something self-evident: if someone is in a slot, no one else is in that slot. Not useful.

B) Formally logically:

R(g) or S(g) or T(g) --> not T(c)
T(c) --> not R(g) and not S(g)

...however, if Tina is a center, Ozzy doesn't have to even play! Remember, if I want the same effect as rule 5, I want to know that if Tina's center, Ozzy's a guard; and if Ozzy's not a guard, Tina can't be center.
(Proof? with this rule, the following situation could be possible:
R(f) S(f) T(c) m(g) p(g)

C) Again, some logique formelle:

R(g) or S(g) or T(g) --> not O(g)
O(g) --> not R(g) and not S(g) and not T(g)

That doesn't bring about the same effect as rule 5. If this new rule is in play, if Tina is center, Ozzy doesn't have to be guard.
(More proof:
m(f) p(f) T(c) R(g) S(g)

E) To rely upon Rule 3 again, if a woman starts at center, that lady's name is Tina Turner (Proud MARY!). Thus, I'll substitute her in to this rule:

T(c) --> n(g)
not n(g) --> not T(c)

Again, Tina can be center without any obligation for Ozzy to even play:
R(f) S(f) T(c) n(g) m(g)

[noah]

Great discussion so far. A note on four, (and I must admit, I'm not the author of this game -- and I'm sure he'll have something smarter to say): this is a new question type that has been popping up on the last few LSATs, so we're keen to include them when we can. While intimidating, they turn out to be rather simple because of the precision of their meaning. The rule change needs to have the same exact effect on the game -- not the same TYPE of effect. So, if a rule states that G must be before L (to make up an example), the replacement must have that exact effect, albeit without stating that. It cannot add a new restriction as well. I'll admit that it's been a challenge to write these questions, and I'm excited to see what folks think.

One way to consider your answer for 4 is whether the set of possibilities is exactly the same with the new rule as with the old one. On the actual LSAT, that's probably more thought than you have time for, and instead you look for a rule that triggers what you're replacing.

I hope that helps.

[Edit: great explanation stampytherhino. I like the reliance on the contrapositive. Furthermore, what other woman who could play center -- Stevie Nicks? No way.]

[edeiber]

There was a similar question on Saturday's LSAT I shouldn't laugh, that probably means I missed it

[stampytherhino]

Since I started writing an explanation with question #4, I figured I might as well go all the way...

We're forming a five-rockstar basketball team out of a pool of 7 talented recording artists/reality television stars:

4 males (which I'll symbolize as m n p o)
3 females (symbolized as R S T)

and putting those five into three positions: two forwards (f), one center (c), and two guards (g).

R1: Either both starting guards are women, or neither starting guard is a woman.
R2: Either both starting forwards are men, or neither starting forward is a man.

So no co-ed guard or forward duos: either both guards are ladies, or both are dudes, and the same goes for the forwards.

R3: Neither Ronnie Spector nor Stevie Nicks starts at center.

The only possible female center is Tina Turner. (Natch!)

R4: Neither Ozzy Osbourne nor Neil Young starts at forward.

Good choice: neither one can focus their eyes enough to see the basket. However, combining this with rule 2 implies either our forwards are m(f) and p(f), or they're two of the women.

R5: If Tina Turner starts at center, Ozzy Osbourne starts at guard.

Ozzy might be drugged out of his mind, but he's cagey enough to make a great point guard. This is pure formal logic:
T(c) --> o(g)
not o(g) --> not T(c)

Now to the questions!

1. Which one of the following could be a correct assignment of players to starting positions?

(A). Take the rules and apply them to the choices, eliminating them one by one.
R1: Either two dude guards, or two lady guards. This gets rid of...
(E)R(g) o(g) m(f) p(f) T(c)

R2: Only women forwards or only male forwards. This gets rid of...
(B)R(g) S(g) m(f) T(f) p(c)

R3: Ronnie and Stevie are never center. This doesn't get rid of anything.

R4: Neither Ozzy nor Neil can be forwards. This cuts out...
(D)o(g) p(g) m(f) n(f) T(c)

R5: If Tina's a center, Ozzy's a guard. This eliminates...
(C)p(g) n(g) R(f) S(f) T(c)

That only leaves choice A:
(A)R(g) S(g) m(f) p(f) o(c)

2. If Stevie Nicks starts at forward, which one of the following must be false?

(E). If we have one female forward, we have to have two (R2), thus the other one is either R or T. Since we'll only have one female left, we then have to have two male guards (R1).

♂(g) ♂(g) S(f) R/T(f) ?(c)

Thus, (E) is impossible: Ronnie is female (and how! a headshot from 1967: http://is.gd/5fEYO)

3. Which one of the following pairs of assignments would determine the assignment of the remaining positions?

(D). This question is asking if we could infer enough to fill up the entire team by knowing two players' positions. I want to start this question by testing the most likely choices: since the rule that gives the most direction is rule 5, I'll test the two choices with Tina as center first.

(C) If Tina's center, Ozzy is a guard. The forwards, though, could be either Ronnie and Stevie, or Mr. Stipe and Prince. This doesn't fill up the roster.

(D) Again: if Tina's center, Ozzy's a guard. If Michael's a forward, we need another male forward (R2), and it can't be Ozzy or Neil (R4). Thus, the only option is Prince. Last but not least, if we have one male guard in Ozzy, we have to have another, and only Neil is left. This one works!
o(g) n(g) m(f) p(f) T(c)

4. Which one of the following, if substituted for the restriction that if Tina Turner starts at center, Ozzy Osbourne starts at guard, would have the same effect on determining who will start?

(D). Our goal is to find a rule equivalent to rule 5. To review R5:

T(c) --> O(g)
not O(g) --> not T(c)

We want a rule that will have the same effect -- in short, intuition suggests we might want to find something pretty close to the contrapositive. (D) says:

not O(g) --> not R(c) and not S(c) and not T(c)

Combining that with rule 3 means that choice (D) is the contrapositive we were looking for.

The others:

(A) says something self-evident: if someone is in a slot, no one else is in that slot. Not useful.

(B) Formally logically:
R(g) or S(g) or T(g) --> not T(c)
T(c) --> not R(g) and not S(g)

...however, if Tina is a center, Ozzy doesn't have to even play! Remember, if I want the same effect as rule 5, I want to know that if Tina's center, Ozzy's a guard; and if Ozzy's not a guard, Tina can't be center.
Need proof? with this rule, the following situation could be possible:
R(f) S(f) T(c) m(g) p(g)

(C) Again, some logique formelle:
R(g) or S(g) or T(g) --> not O(g)
O(g) --> not R(g) and not S(g) and not T(g)

That doesn't bring about the same effect as rule 5. If this new rule is in play, if Tina is center, Ozzy doesn't have to be guard.
m(f) p(f) T(c) R(g) S(g)

(E) To rely upon Rule 3 again, if a woman starts at center, that lady's name is Tina Turner (Proud MARY!). Thus, I'll substitute her in to this rule:
T(c) --> n(g)
not n(g) --> not T(c)

Again, Tina can be center without any obligation for Ozzy to even play:
R(f) S(f) T(c) n(g) m(g)

5. Which one of the following could be true?

(C). The first two of these might jump out as being impossible, numbers-wise:
(A) doesn't work: if we have one woman, she has to be center (any other single lady must be paired up to play forward or guard: Beyonce isn't part of this game.)
(B) is impossible: if we have two women play, and Tina is center, we only have one other woman -- and we need a pair to play either forwards or guards.

But then we hit pay dirt:
(C) If Tina is guard, that means the other guard is Ronnie or Stevie. With two of the female players accounted for, we must have two males be forwards, and as per rule 4, neither Ozzy nor Neil can play forward, and thus the forwards must be Michael and Prince. For center, we have Neil or Ozzy:
m(f) p(f) n/o(c) T(g) R/S(g)

The other two don't work at all.
(D) If we have three women, and Tina's a guard, Ronnie or Stevie will end up as a single lady: and since neither of them could be center, this won't work.
(E) If Michael's a forward, then Prince is too (R2 and R3); with three women, we end up in the same situation as we did in (D).

6. If Ronnie Spector starts at guard, how many different starting line-ups are possible?

(B). If Ronnie's a guard, then either Stevie or Tina is a guard, too. This means we have male forwards, and only Michael and Prince can fit that bill. Thus, for center we've got Neil or Ozzy (but not Tina: since Ozzy's not a guard, we can't have Tina as center):
m(f) p(f) n/o(c) R(g) S/T(g)

This gives us four possibilities, or choice (B).

7. If the tournament decides to change the rules and require the team to add a sixth starter"”a second center who must be female"”and all the other rules remain in effect, which one of the following must be false?

(C). This adds a wrinkle, but nothing serious (although it's arguable this would ruin the entire game of basketball). The only center who can be female is Tina, so we have Ozzy as a guard, and one of the other men as the other guard. Moreover, since Tina was the only possible female center, that means the other center has to be male. That makes for three males assigned (two guards, and one center), and because we only have one male left over, the remaining females (Ronnie and Stevie) have to be forwards:

R(f) S(f) T(c) ♂(c) o(g) ♂(g)

A quick scan shows us that (A) is possible, and (B) is necessary; however, a quick scan of our setup shows that (C) isn't possible at all!

BONUS QUESTION:

8. Which ridiculous diva-quality demand in the contract rider will make it so no team can possibly be formed?

(A) Ozzy and Neil cannot be on the team together (will wander off behind the bleachers).
(B) Ronnie must be on the team, but refuses to be on the team with Tina (due to a long-standing argument about Phil Spector).
(C) If Stevie is included on the team, neither Ozzy must not be included (danger of relapse).
(D) Females must play guards, and neither Ozzy nor Neil can be center (Prince's whims).
(E) No females can play forwards or guards (Ozzy didn't feel comfortable with it).

The answer is (D): the other choices work out just fine. So if we have female guards, we have to have male forwards (R2); if we have male forwards, they've got to be Michael and Prince (R4). If that's the case, none of the three players left to play center don't work: Ozzy or Neil (nope! can't be center, so the answer choice says) or Tina (the only possible female center -- but she won't work because of the contrapositive of R5).

(A) It's not so difficult to leave one of them out of the team altogether, and we'll be fine.
m(f) p(f) o(c) S(g) T(g)

(B) There's got to be a story there, but if Ronnie is a forward with Stevie this works fine.
R(f) S(f) o(c) n(g) p(g)

(C) Sensible, and not terribly restrictive. Here's one way it can play out:
R(f) S(f) T(c) m(g) p(g)

(E) This works out okay:
m(f) p(f) T(c) o(g) n(g)

[ManhattanPrepLSAT2]

Great job everyone --

One of the reasons we don't give away written out solutions is that we feel this type of back-and-forth debating is a great way for the people who post and the people who read the posts to develop and strengthen the mental processes that are necessary for logic games.

Thinking about competing ideas and explanations, and determining, for yourself, what is correct or incorrect, what solutions have sound reasoning and what solutions have some holes, is going to have a stronger impact than, say, simply reading an explanation that you already know is correct.

I don't think I need to add anything much more to the debate/written solutions -- those of you who have posted have done a terrific job of breaking this game down --

I'll just add one thing: if you are still struggling with this game, you might consider trying it using a few frames. In terms of gender, there are three ways in which the positions can be filled:

GGFFC could be...

WWMMM

MMWW?

MMMMW

You can infer quite a bit about each of these frames from the initial constraints, and, if you have the them set up correctly, these frames can make the job of answering questions much easier.

[jmichaelchin]

Not sure we'll ever see a similarly themed game on the real LSAT. But it was an interesting one. Here is my conceptual explanation.

Game:

Grouping, no linear component, some conditional rules. overloaded such that there are 7 variables for 5 spaces. 2 won't get used (until the game changer). Also the variables aren't all the same, we have females and males and the grouping component is variegated as well.

As for the overloaded aspect, it would be good to keep in mind that 2 variables won't fit. I didn't really use this that often.

Lots to keep in mind, but then again, these fortnightly problems are usually not simple ones.

Diagrammatics:

I diagrammed this out with the five positions


___ __ __ __ __
C F F G G
{not {not O,N}
R, S}

with some natural separation between the positions. A couple of the rules go right on the diagram, with N and O not being allowed as forwards. Also, R and S cannot be Centers leaving just T for that (Natch, as was mentioned above).

I also wrote out the female guard rule: FemG <--> FemG, as well as the contrapositive (can't figure out how to do strikethrough text on there)

With the male forward rule we can use actual names since we know N and O can't be there anyway so: R(forward) <--> S(forward) and the contrapositive.

Finally, the rule I forgot about when I initially did it and really screwed me up: Tc --> Og and the contrapositive of that. This really came in handy and if you forgot about it then it could really slow you down.

Key things to try to keep in mind while working the questions:

1. Tina is the only female that can be center and when she is Center, O is a G, and therefore another female can't be aG

2. The female guards and male forwards. If ANYONE is placed in these positions it can lead to serious inferences since,
-you know the gender of the person in the other of that position
-that exhausts a lot of a gender group so it can make the other positions more restricted.
-Forward is especially restricted since of the males, only R and S can go there.

--> this is a general rule when working these things, keep an eye on the points of restriction.

I don't think there are any other big deductions and from glancing at other people's responses it doesn't seem like they found any.

Questions:

1. Start with the easiest to visualize.

-Right off the Bat N is a Forward, so Eliminate D.
-Now I looked at Male forwards and saw a mismatch on B - M with T, Eliminate B
-Female guards mismatch, eliminate E
-Final rule, Tc-->Og and predictably this kills C
( I was stupid and didn't read the Tina center rule at first so this had me pulling out my hair. You've got to be careful in the diagrammming b/c a small F up can cost you big. I have to try to find a better balance between speed and accuracy)

2. Starter's pistol. Make a small side diagram and add S as a forward. You know R/T is the other forward. So think, big restrictions - this means you can't have a girl as a guard because there aren't enough to pair up.

No need to plug in, just go straight for E

3. My gut instinct on a global question like this with so many options is to panic. That really hurt me on time as well, but looking back on it, I think the best idea is try to ignore the panic and look for a pattern in the options. When doing that, I noticed the latter two (D,E) had S as a forward. Comparing those two, I saw E had S with P as forwards, which is not very helpful since if S is a forward, P has to be a forward anyway. But D was interesting because it had S as a forward and T as a Center. T as a center also leads to a big inference, so I quickly diagrammed this, which showed this led to an all male backcourt and forwards with Tina as center. bingo!! don't panic!!

4. I originally got this wrong, but of course, in hindsight it's not that bad. (also, it seemed early in the game for one of these mindfu$#ers

I WAS RIGHT, however, in noticing that it's a rather specific rule, that would seem to have specific consequences. So it would probably need to be a very similar change.

My gut said that E was right because T was the only woman who could play center anyway, so the sufficient condition was effectively the same. i also figured that N and O in all of the rules were interchangeable, so why not pick that? Well of course, it would change the game that if Tina was Center then N would have to be a G instead of O. Stupid, right?

Later, I realized I should have read more carefully (I was worried about time) and seen that D was the contrapositive and thus had to be right. Made me feel stupid.

5. this one was actually not that bad. with a working knowledge of the female and male forward-guard rules, you could pretty much run through the rule without diagramming. just keep your cool!

A - sounds good until it says N is center. That would force a mismatch at forward or guard and thus Eff us

B - Starts off fine, but then the Tina thing also forces a mismatch. if you didn't have a good understanding of those female male rules, this whole game could take an eternity!

C - It's perfect. Just stop there. A risky move but I find every second counts in these godforsaken things.

6. I got this one wrong initially and you'll see why.

So this is easy to diagram.

R goes as a guard.
R/T is a guard
M, P forced into forwards
N/O is center.

You don't have to be a math major to realize that's four options so (B)

You see, I originally forgot about the T center rule, so I had her penciled in there as a center, making 6 options. but of course, that would force O to be a guard and he's a man so he can't be with R there. Man, I'm stupid sometimes.

7. Man these atlas games are devious. two gamechangers in one game! I guess if you can kill these games fast, you are a shoo-in to -0 your actual LG section. Is that right guys?

I got this wrong and read it as must be true. so of course, several fit that bill and picked the first one that stuck out. I really choke when my timer is on.

In reality it's not that bad. Just add an extra Center line and see what happens.

Well we know T is one of the centers and the other has to be a dude. that T is a center means O is a guard. Which means another male is a guard. Now since 3 of the males are accounted for (2nd center, both guards) we can't have one at forward, meaning R and S are at forward. I put MNP placeholders at the 2nd guard and 2nd center positions to remind me.

Anyway, attacking the problems from there C stands out as impossible given this diagram. pick it!


So a tough game, I'd say. No real explicit rule linkage but some serious areas of restriction help. took me 20 minutes with 2 errors on the first go around. Hopefully, making this guide helps others and me!

Thanks Atlas!