Arithmetic Puzzle on Mental Calculation

A man entered a store and spent one-half ofthe money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as he had cents when he went in. How much money did he have on him when he entered?

What is the largest sum of money-all in current coins and no silver dollars-that I could have in my pocket without being able to give change for a dollar, half dollar, quarter, dime, or nickel?

“When I got to the station this morning,” said Harold Tompkins, at his club, “I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel’s worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a newspaper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?”

If you add the square of Tom’s age to the age of Mary, the sum is 62; but if you add the square of Mary’s age to the age of Tom, the result is 176. Can you say what are the ages of Tom and Mary?

When visiting an insane asylum, I asked two inmates to give me their ages. They did so, and then, to test their arithmetical powers, I asked them to add the two ages together. One gave me 44 as the answer, and the other gave 1,280. I immediately saw that the first had subtracted one age from the other, while the second person had multiplied them together. What were their ages?

Here is an example of the sort of “Breakfast Problem” propounded by Metrodorus in 310 A.D. Demochares has lived one-fourth of his life as a boy, one-fifth as a youth, one-third as a man, and has spent thirteen years in his dotage. How old is the gentleman?

Rackbrane said the other morning that a man on being asked the ages of his two sons stated that eighteen more than the sum of their ages is double the age of the elder, and six less than the difference of their ages is the age of the younger. What are their ages?

A boy on being asked the age of himself and of his sister replied:
“Three years ago I was seven times as old as my sister; two years ago I was Age Puzzles 13
four times as old; last year I was three times as old; and this year I am two
and one-half times as old.”
What are their ages?

“How old are you, Robinson?” asked Colonel Crackham one morning. “Well, I forget exactly,” was the reply; “but my brother is two years older than I; my sister is four years older than he; my mother was twenty when I 14 Arithmetic & Algebraic Problems was born; and I was told yesterday that the average age of the four of us is thirty-nine years.” What was Robinson’s age?

Between two and three oclock yesterday,” said Colonel Crackham, “I looked at the clock and mistook the minute hand for the hour hand, and consequently the time appeared to be fifty-five minutes earlier than it actually was. What was the correct time?”