A Flock of Sheep and a Camel: answer
The answer is:
Four shekels.
Assume that there are N sheep. For each sheep the price is N
shekels, so the total value of the flock is N² shekels. As the
remainder of currency after dividing the 10 shekel coins so that Isaac
gets one more of them is a few coins, the task is to find what values
N² mod 10 can have when the number of tens is odd (i.e. N² mod 20 >
10). Surprise: this condition is only met when N is of the form
(m*10)+4 or (m*10)+6 (m is a positive integer). And in all these cases
the leftover is 6 shekels. Therefore, the camel is worth four shekels.
E.g:
- 12² = 144 (number of tens even, won't do)
- 13² = 169
- 14² = 196 (number of tens is odd, OK)
- 15² = 225
- 16² = 256 (OK)
- 17² = 289
- 24² = 576 (OK)
- 26² = 676 (OK)
So N belongs to the series 4, 6, 14, 16, 24, 26, 34, 36...
Unfortunately my mail PC's disk broke permanently in December 1998,
the backup copies did not have even close to all the mails I had
received, and therefore I cannot give a list of all people who
submitted correct answers to this problem. Sorry!
Njet Problem Collection
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