Friday, November 16, 2018 0

Sam Lloyd was born in Philadelphia in 1841, but lived most of his life in New York. He was primarily a chess player and composer of chess problems, but he also delighted in mathematical puzzling. Actually, not just mathematical puzzles, but word puzzles; picture puzzles; tangrams; he composed thousands of them. In fact, it was one of his pictorial puzzles which grabbed my attention at a very early age, and possibly sparked my enjoyment of such puzzles. Have a look at it here: you will need to print off the picture and cut out the shapes! (You do need to try and solve the puzzle yourself before looking at the solution.)

So here are some of Sam Lloyd’s mathematical puzzles – no easier now than when he first composed them.

Puzzle 1:   A bicycle rider went a mile in three minutes with the wind, and returned in four minutes against the wind. How fast could he ride a mile if there was no wind?

Puzzle 2:   A gypsy queen who ekes out a precarious existence by gathering quarters from gullible victims who want the future revealed, laments the decline of the fortune-telling industry as follows: ‘The week before last I earned less than three dollars, last week only a third as much as the previous week and this week somewhat less than half as much as the week before.’

How much did she earn in three weeks? (Giveaway note: A quarter is a quarter of a dollar.)

Puzzle 3:  An Arab Sheik, finding himself about to die, called his sons about him and said: ‘Divide my camels among you in the proportion of one-half of the herd to the eldest son, the second son one-third, and to the youngest son one-ninth.’
Thereupon the oldest son cried: ‘O, my father, one-half, one-third, and one-ninth do not constitute a whole. To whom, therefore, shall the remainder of the herd be given?’

‘To any poor man who may be standing by when the division is made,’ replied the Sheik, who thereupon died.

When the herd was collected a new difficulty arose. The number of the camels could not be divided either by two or three or nine. While the brothers were disputing, a poor but crafty Bedouin, standing by with his camel, exclaimed, ‘Behold, I will sell you my beast for ten pieces of silver, so that you may then divide the herd.’

Seeing that the addition of one camel would solve the difficulty, the brothers jumped at the offer, and proceeded to divide the herd, but when each had received his allotted portion there yet remained one camel.

‘I am the poor man standing by.’ Said the crafty Bedouin, and gaily mounting the camel, he rode away, with the ten pieces of silver in his turban.

Now, how many camels were in the Sheik’s herd?

(Not actually a very hard puzzle, but such a surprising outcome!)