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Miscellaneous Puzzles on Mental Calculation Set 2

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Three juvenile highwaymen, returning from the market town movie house, called upon an apple woman "to stand and deliver." Tom seized half of the apples, but returned ten to the basket; Ben took one-third of what were left, but returned two that he did not fancy; Jim took half of the remainder, but threw back one that was worm eaten. The woman was then left with only twelve in her basket. How many apples had she before the raid was made?

Correct! Wrong!

The woman must have had 40 apples in her basket. Tom left her 30, Bob left 22, and Jim left 12.

The officer must have had 1,975 men. When he formed a square 44 X 44 he would have 39 men over, and when he attempted to form a square 45 X 45 he would be 50 men short.

Correct! Wrong!

An officer arranged his men in a solid square," said Dora Crackham, "and had thirty-nine men over. He then started increasing the number of men on a side by one, but found that fifty new men would be needed to complete the new square. Can you tell me how many men the officer had?"

Professor Rackbrane asked his young friends the other morning if they could find three whole numbers in arithmetical progression, the sum of every two of which shall be a square.

Correct! Wrong!

An answer is as follows: 482, 3,362, 6,242, which have a common difference of 2,880. The first and second numbers sum to 622, the first and third to 822, and the second and third to 982

Professor Rackbrane, when helping himself to cream at the breakfast table, put the following question: "An honest dairyman found that the milk supplied by his cows was 5 per cent cream and 95 per cent skimmed milk. He wanted to know how much skimmed milk he must add to a quart of whole milk to reduce the percentage of cream to 4 per cent

Correct! Wrong!

Half a pint of skimmed milk must be added

Find two different numbers such that the sum of their squares shall equal a cube, and the sum of their cubes equal a square

Correct! Wrong!

If we make one number 625m6, and the other number double the first, we can get any number of solutions of a particular series. Thus, if we make m = 1, we get the answer 6252 + 1,2502 = 1253, and 6253 + 1,2503 = 46,8752.

Aunt Martha bought some nuts. She gave Tommy one nut and a quarter of the remainder; Bessie then received one nut and a quarter of what were left; Bob, one nut and a quarter of the remainder; and, finally. Jessie received one nut and a quarter of the remainder. It was then noticed that the boys had received exactly 100 nuts more than the girls. How many nuts had Aunt Martha retained for her own use?

Correct! Wrong!

There were originally 1,021 nuts. Tommy received 256; Bessie, 192; Bob, 144; and Jessie, 108. Thus the girls received 300 and the boys 400, or 100 more, and Aunt Martha retained 321.

"What number is that," Colonel Crackham asked, "which, added separately to 100 and 164, will make them both perfect square numbers?"

Correct! Wrong!

If you add 125 to 100 and also to 164, you get two square numbers, 225 and 289, the squares of 15 and 17 respectively

Dora Crackham the other morning asked her brother this question: "If three boys had a hundred and sixty-nine apples which they shared in the ratio of one-half, one-third, and one-fourth, how many apples did each receive?" 206

Correct! Wrong!

Colonel Crackham, one morning at the breakfast table, said that two men of his acquaintance can saw five cords of wood per day, or they can split eight cords of wood when sawed. He wanted to know how many cords must they saw in order that they may be occupied for the rest of the day in splitting it.

Correct! Wrong!

The men must saw 40/13 cords of wood

George Crack ham put five paper bags on the breakfast table. On being asked what they contained, he said: "Well, I have put a hundred nuts in these five bags. In the first and second there are altogether fifty-two nuts; in the second and third there are forty three; in the third and fourth, thirty-four; in the fourth and fifth, thirty." How many nuts are there in each bag

Correct! Wrong!

The five bags contained respectively 27, 25, 18, 16, 14 nuts. Each bag can be found by subtracting the other two pairs together from 100. Thus, 100 - (52 + 30) = 18, the third bag

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