error in challenge question 08/26/02

[jigar24]

In the game Cako, a player is awarded one tick for every third Alb captured, and one click for every fourth Berk captured. The total score is equal to the product of clicks and ticks. If a player has a score of 77, how many Albs did he capture?

(1) The difference between Albs captured and Berks captured is 7.

(2) The number of Albs captured is divisible by 4.


The statements contradict each other

[mschwrtz]

You need to say more about the supposed contradiction.

Do you assume that the number of Albs captured must be a multiple of 3, and the number of Berks captured a multiple of 4? On that assumption the two statements do contradict one another, but there's no reason to make that assumption.

[jigar24]

Hi mschwrtz,

I think you've misunderstood the question. Don't see why need to make any assumptions here..

Let me give you the scene first,

Albs = A
Berks = B

For every 3A player gets 1 Tick(T)
For every 4B player gets 1 Click(C)

So for example there are 6A and 8B
AAA AAA
T T
BBBB BBBB
C C

Total points is product of T and C..
So in our example total points is 2 X 2 = 4

Now, according to the question,
Total points = 77
So if you factorize 77 there are 4 possibilities of T and C

1T X 77C
7T X 11C
11T X 7C
77T X 1C




Clicks Albs Captured Ticks Berk Captured
1 3, 4 or 5 77 308, 309, 310, or 311
7 21, 22, or 23 11 44, 45, 46 or 47
11 33, 34, or 35 7 28, 29, 30 or 31
77 231, 232 or 233 1 4, 5, 6, or 7

If we look at statement 1,

it says diff between Albs and Berks is &
So ONLY option is 35 Albs and 28 Berks..

Now Statement two says Albs captured is divisible by 4.. which cannot be true.. as only possible number of Albs is 35 and it NOT divisible by 4

[graphica]

(1) The difference between Albs captured and Berks captured is 7.

Does this statement necessarily means that 3A=4B-7?

Can it also mean:
4B=3A-7

Because the statement one says that difference between Albs captured and Berks captured is 7, it doesn't specifically says that the Albs captured are 7 more than Berks captured.

Sorry if my ques is lame!

[mschwrtz]

Ah, I see. yes, as you've recorded these statements they do contradict one another. Fortunately, they don't contradict one another as they're written in the challenge bank.

Check it out, here's what it actually says:


(1) The difference between Albs captured and Berks captured is 7.

(2) The number of Albs captured is divisible by 5.