18. The Tigers and the Bears played a game; the total number of points scored by both
teams was 115. The Bears won and their score is interesting: if we divide it by two,
the remainder is 1; if we divide it by 3, the remainder is 2; if divide it by 4, the
remainder is 3; if we divide it by 5, the remainder is 4; if we divide it by 6 the
remainder is 5. What was the score of the teams?

The problem has told us that when divided by 2,3,4,5, and 6 you will get a certain remainder. Saying that the problem tells us that all the multiples of 2,3,4,5, and 6 are not the answer. Also knowing that the bears won we know that it has to be more that 57 since the tigers have got to have less points. So now we are left with the numbers: 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, and 113. Since they didn't give us anymore clues we have to eliminate answers by ourselves the rest of the way. Of course I started with 59 since it was the closest. We would already know that 59 divided by 2 would equal 1 knowing it is an odd number.

59 ÷ 3 = 2

59 ÷ 4 = 3

59 ÷ 5 = 4

59 ÷ 6 = none other then 5

Right away from these results you would know that 59 is the right answer! But just in case it wasn't I checked and it still showed that the answer was 59. Therefore I believe the answer to this question is 59