71. There is a certain number whose third and fourth powers, taken together,
exhibit all the digits from 0 to 9, each once and once only. Can you work out what the number is?

The third and fourth powers must contain 10 digits between them, so the number sought can only be 18, 19, 20, or 21. Of these, 20 and 21 are bound to duplicate zeros and ones, respectively. Testing 18 and 19 reveals that 18 is the answer. The third power of 18 is 5832, and the fourth power of 18 is 104,976.

72. Arlene has found a cut-rate florist's shop where she can buy 6 poinsettias
and 5 lilies for $61, or 5 poinsettias and 6 lilies for $60. How much will she have to pay for a dozen lilies?

$60. Lilies are $5. each and poinsettias are $6. each.

73. What is the next number in the following sequence?

4
8
32
128
2,048 ?

8,192 or 2 to the 13th power. The sequence is built on the number 2 being raised to the consecutive prime numbers. 2 to the 2nd power = 4; 2 to the 3rd power = 8; 2 to the 5th power = 32; 2 to the 7th power = 128; etc.

74. Sally has twice as many sisters as she has brothers. Her brother
Patrick has five more sisters than he has brothers. What is the least number of girls and boys in the immediate family that fits the above configuration?

3 boys and 7 girls. Sally has six sisters and three brothers. Each brother has two brothers and seven sisters.

75. John gets to spend the rest of his math class time in the
library if he can solve the sequence below. Can you help him?

8, 61, 42, 23, 04, 84, ?

65. These are multiples of 8 with the digits reversed.

76. What is the number that is 2 more than one-tenth of one-fifth of one-tenth of 1,000?

4. (1,000 ÷ 10 = 100 ÷ 5 = 20 ÷ 10 = 2 + 2 = 4).

77. Replace the asterisks with mathematical symbols to make this equation work.

888 * 8 * 8 * 88 * 8 * 8 * 8 = 1527

888 - (8 x 8) + 88 - 8/8 = 1527.

78. In a contest to guess the number of balloons in a bunch, Alice guessed 31, Betty
guessed 29, Carol guessed 23, Denise guessed 25, and Edith guessed 27. Two were wrong by 2, and two were wrong by 4. The other was correct. How
many balloons were there and who guessed right?

Edith guessed correctly that there were 27 balloons.

79. Charley bought a motorcycle to tour the country with. After two years, it
had depreciated to $6,000 and in five years it had a book value of $3,750. What did the motorcycle cost originally, and how long before it would have a book value of $0?

Original cost was $7500, and 10 years after the purchase it will have a book value of $0. Depreciation is $750 per year.

80. My wife and I can't seem to get our watches to work properly. Hers
consistently runs one minute per hour fast, and mine runs two minutes per hour slow. This morning we nearly missed a wedding because our watches were an
hour apart and we looked at the slower one. How many hours had elapsed since we set both of them properly?