Miscellaneous Puzzles on Mental Calculation
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A boy is to be choseA certain division in an army was composed of a little over twenty thousand men, made up of five brigades. It was known that one-third of the first brigade, two-sevenths of the second brigade, seven-twelfths of the third, ninethirteenths of the fourth, and fifteen-twenty-seconds of the fifth brigade happened in every case to be the same number of men. Can you discover how many men there were in every brigade?
n president and a girl vice-president of the senior class of a school. In how many ways is this possible if the class has twelve boys and ten girls?CorrectIncorrect
A man said the house of his friend was in a long street, numbered on his side one, two, three, and so on, and that all the numbers on one side of him added up exactly the same as all the numbers on the other side of him. He said he knew there were more than fifty houses on that side of the street, but not so many as five hundred. Can you discover the number of that houseCorrectIncorrect
A man married a widow, and they each already had children. Ten years later there was a pitched battle engaging the present family of twelve children. The mother ran to the father and cried, “Come at once! Your children and my children are fighting our children!” As the parents now had each nine children of their own, how many were born during the ten years?CorrectIncorrect
What is the third lowest number that is both a triangular number and a square? Of course the numbers 1 and 36 are the two lowest that fulfill the conditions. What is the next number?CorrectIncorrect
This is the kind of question that was very popular in Venice and elsewhere about the middle of the sixteenth century. Nicola Fontana, generally known as “Tartaglia” (the stammerer) was largely responsible for the invention. If a quarter of twenty is four, what would a third of ten be?CorrectIncorrect
Colonel Crackham asked the junior members of his household at the breakfast table to write down five odd figures so that they will add up and make fourteen. Only one of them did it.CorrectIncorrect
When stopping at Mangleton-on-the-Bliss the Crackhams found the inhabitants of the town excited over some little local election. There were ten names of candidates on a proportional representation ballot. Voters should place No. I against the candidate of their first choice. They might also place No.2 against the candidate of their second choice, and so on until all the ten candidates have numbers placed against their names. The voters must mark their first choice, and any others may be marked or not as they wish. George proposed that they should discover in how many different ways the ballot might be marked by the voterCorrectIncorrect
Can you find,” Professor Rackbrane asked, “two consecutive cube numbers in integers whose difference shall be a square number? Thus the cube of 3 is 27, and the cube of 2 is 8, but the difference, 19, is not here a square number. What is the smallest possible case?”CorrectIncorrect
If we wanted to find a way of making the number 1,234,567 the difference between two squares, we could at once write down 617,284 and 617,283a half of the number plus’ll and minus Ih respectively to be squared. But it will be found a little more difficult to discover two cubes the difference of which is 1,234,567.CorrectIncorrect
Can you find two three-figure square numbers (no zeros) that, when put together, will form a six-figure square number? Thus, 324 and 900 (the squares of 18 and 30) make 324,900, the square of 570, only there it happens there are two zeros. There is only one answer.CorrectIncorrect