101. The local grocer is a would-be mathematician. He likes to arrange his
apples in nice rows. However, when he lays his apples in rows of 3 he has one left over. When he lays them in rows of 5 he also has one left over. Remarkably
he also has one left over when he arranges them in rows of 7 and 9. 11 seems to be the magic number, for, in rows of 11 there are no apples left over. How many
apples does the grocer have?

102. Which of these numbers is the odd one out?

27 6 11 38 19 51 66 83

19. All of the other numbers are 2 greater than a square number, that is, a number produced by squaring an integer. For example, 27 = 5 squared + 2.

103. If three typists can type 9 pages in one and a half hours, how many pages can nine typists type in 3 hours?

54 pages. Each typist can type 3 pages in a hour and a half. This means that each typist can type 6 pages in 3 hours; so 9 typists in 3 hours would be able to type 54 pages.

104. The numbers on a die are not placed at random. On every pair of opposite
faces the sum of the numbers is 7: 6 is opposed to 1, 5 to 2, and 3 to 4.

There are several other ways of placing six numbers on a die. How many ways are there altogether?

We can place the number 1 anywhere. Then there are five ways of choosing the number which will be opposite the 1. Imagine that the 1 and its opposite are on the top and bottom of the die. We still have to place the four remaining numbers on the four remaining faces around the die. Let X be one of these numbers. There are three ways of choosing its opposite number. Then there are two ways of placing the last two numbers. The total number of ways is: 5 x 3 x 2 = 30. None of these 30 dice can be turned into one of the others by rotating it in any direction.

105. If a crab and a half weigh a pound and a half, but the half crab weighs half
as much again as the whole crab, what do half the whole crab and the whole of the half crab weigh?

2.1 pounds. The whole crab must weigh 0.6 pounds, and the half crab 0.9 pounds, totaling 1 1/2 pounds. If the former were halved and the latter doubled, the weights would then be 0.3 and 1.8 pounds, totaling 2.1 pounds.

106. James is now his mother's age if the digits are reversed. Only a year ago, James was exactly one-half his mother's age. How old are they now?

James is 37, his mother is 73. A year ago he was 36 and she was 72.

107. If you had a piece of paper that was 0.001 inch thick, how tall a pile would it make if it was doubled fifty times?

108. Find the number that best completes the following sequence.

1 4 9 16 _ 36 49

25. The numbers are the squares of 1, 2, 3, 4, 5, 6, and 7.

109. What number gives the same result when it is added to 1 1/2 and when it is multiplied by 1 1/2?

110. What is the number that is 5 more than one-half of one-quarter of one-half of one-quarter of 16,000?

255. (16,000 ÷ 4 = 4,000; ÷ 2 = 2,000; ÷ 4 = 500 ÷ 2 = 250; + 5 = 255).