PUZZLE COLUMN.

Ashburton Guardian, Volume VII, Issue 1972, 17 October 1888, Page 3

PUZZLE COLUMN.

THB FIFTEEN YOUNG LADIES PCZZ r .E. Fifteen young Udiea attend a boarding ■cho 1. 'i he mistress wishes them to go ont for a walk each day In the week In five parties of three efch, bu f , as she has reason to fear conspiracy agaloat the order of the school, will not allow any two to go together more than pnoe during the week ( >f aeven dajß ) Every girl has to go oat on each of tbe seven days, and always three together. How did the the mistress arrange them each day 1 A TBICK WITH FIGURES. The following mathematical trick, from La Natnre, although not new, may be revived for the benefit of those who are unaqualnted with It It never falls to mystify thoae who do not understand it. Tell a person to select any even number of figures, and, without letting you see them, to write them down and then place under them the same figures In reverie order, Thus for example ; — 943518 815349

This done, ask him to add the two namberß, and to give you the earn, less •ny figure whioh he may ohoose to rejaot, and the spsoe occupied by which must bo left blank or shown by a hyphen. For example, 17688-7. Patting od an inspired air, you now assort that the figure o.nitted 18 6 If you prefer, you can let toe person subtract one numbei from the other, and then tell him the omitted figure with the same ease. Tue trick is simple, and the explanation of It oan be understood by any boy who haa studied arithmetic. The Bum of a number and the same number reversed is a multiple of 11, and their difference is a multiple ot 9. Now, la multiples of 11, the sum of the even figures is equal to that of the odd odob. Applying this rule to our example, 17588-7, and representing the unknown figure by x, we have xtßt7=lt7tstß=2l. A sin? pie mental calculation gives x=6. Where the number of figures m tbe product Is an even one, the sum of tbe first two or first three will equal the sum of the last two or last three, and so on. Proceeding with the d fference, which Is a multiple of 9, the Bum of the figures must itself be a multiple of 9, Taking our example, 1.8165, and adding the figures, we obtain 25, but as this is not a multiple of 9, ire have to add 2 to obtain the multiple, and thia was the figure rejected.