ALL PUZZLISTS ARE familiar with the ancient story of thirty Christians and Turks at sea in a storm, and how the captain decided that one-half of his passengers would have to be thrown overboard to save the ship. Being a fair-minded man who believed that all should be treated impartially, he arranged them in a circle and agreed to count off every thirteenth man until fifteen unfortunate mortals had been selected. As the story goes, one of the Christians was a mathematician and a devout man who believed that Divine Providence had sent him to save the faithful and destroy the unbelievers. Therefore he arranged the thirty passengers in such a manner that the thirteenth man, as the counting out proceeded, invariably proved to be a Turk.
That puzzle, as you doubtless remember, turns upon arranging let us say fifteen white counters and fifteen black in a circle, so that by counting round and round and taking away every thirteenth one, that all of the blacks will be removed. To solve the puzzle you need merely place thirty counters in a circle and begin to count around picking off every thirteenth until fifteen have been removed. Then replace the vacant spaces with black men and let the other fifteen be white and it shows how the Christians and Turks must have been arranged.
The above story is related by way of introduction to tell how it chanced one day that ten children, five girls and five boys, returning from school, found five pennies. A little girl found the money, but Tommy mutton-head claimed that as they were all together the “find” really belonged to the crowd. He had been told the “Christians and Turk” story, and thought it would be a great scheme to play it as a game in dividing up the pennies, it being clear that there were only enough to go half way around. He placed the children in a circle, as shown in the picture, and told the girls that they were the “Christians" and the boys the “Turks. ” Tommy had planned it all right, so that by counting thirteen from a circle point the girls would all be counted out, but he forgot that each girl got a penny as she was counted out, so the boys were left, and all that Tommy got was a good licking which the boys gave him in a lot back of the school. Now this puzzle differs from the old Christians and Turks problem, because you are to guess the proper starting point, as well as the smallest number which will count out the boys and leave the girls.
Commencing with the upper girl without a hat and counting around to the right, every thirteenth will be a girl, but the puzzle is to tell what number Tommie should have used in place of 13 to give the prizes to the boys.
Of course, as each one is counted out, he is supposed to step back from the circle and is omitted in the next counting, which commences from the next one.
This puzzle is just the reverse of the ordinary story of the Turks who were thrown overboard, as in that problem the point is to arrange the men in a circle so that every thirteenth man would be a Turk, while in this puzzle the question was to find the best number as well as the correct starting point, to count out all the boys.
As discovered by some of our clever puzzlists, the solution is obtained by commencing the count with second girl from the left in the upper part of the circle, and, counting her as No. 1, continue to the right counting off every thirteenth one. This method will count out all the girls and the boys will be “left,” but if you wish to count out only the boys, so the girls will be left, use fourteen in place of thirteen, so that by picking out every fourteenth boy, they would have got the pennies and Tommy Muttonhead would have escaped the licking.
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