FOR THE CHILDREN.

New Zealand Herald, Volume XLIV, Issue 13393, 23 January 1907, Page 9

FOR THE CHILDREN.

Sd.Mi: thicks WITH EH it'll i s

" Now. Uncle Hob,'' said Lucy. " 1 have * new pencil and a whole new pad of paper, and it you please I'd like a new puzzle."

"Very well, then,"' said Uncle Bob. "do just as I tell you. Von and Fred each write un your paper a row of figures." So Ltiev wrote 8, 6, 3, 2, J. 4 ; and Fred wrote 4, 6. 7. 9, 8, 6. 1, 4.

"Now, then," went on Uncle Hob, "add up those digits in your head, and subtract the sum from your original number."

So Lucy added up her digits, and found they came, to 24. Subtracting this from her original number, sin; had left 865,190; while Fred, whose digits added up to 42, subtracted, and had a remainder of 43,798,572.

"Now strike out one figure from your answer,' said Uncle Mob, "and write on another slip of paper your answer, with that figure; omitted."

In a moment Lucy had struck out the liume 6 and handed her uncle the slip of pa per,' on which was written 83.190.

Alter a brief glance at. it, Uncle Hob said quietly, "You struck out the figure 6." "So I did!" said Lucy, opening her eyes ill amazement.

.Meantime-Fred had struck 8 out of his answer, and offered lor his uncle's inspection the figures 1.379.572.

" You crossed oil' 8," said Uncle Hob. "1 did so," said Fred. " Please try it. again."

So they tried it again, and this time when the children were about to present their lines of figures to him for inspection Uncle Hob said, "You may write the lines of figures as you have them, or you may write them ward, and you need not tell me which."

Lucy reversed her line of figures and gave it to her Uncle; but Fred gave his just as he had it on his own paper. It seemed to make no difference; for Uncle Boh told them instantly what figures they had crossed out. Then they tried it a third lime, and, to puzzle them still further, Uncle Hob told them that they might jumble their figures all up, and, as long as they kept the, real figures they had. they might offer them to him in any rotation. This time Lucy's original row had read 9, 2, 3, 6, 4. 8. 1.

! lie sum ol these digits was 33, and consequently, after subtracting, she had 9,236,448. She struck out one of the 4's and mixed up the others, so that they stood 863.942. 'J.his row she handed to her uncle, who immediately told her that she had crossed off a 4.

I'red had taken a short number this time, lie had put down only 6, 3. 2, 1,4. These digits amounted to 16. After subtracting, he had remaining 63,198. He crossed out the 9, and, mixing up the others, gave his uncle the row, 1683.

Uncle Bob looked at it abstractedly. Then he closed his eyes. "1 iseem to see' a 0 floating in the air," he said. "I think, my boy, you crossed off a 0." "No, sir!" cried Fred triumphantly. Ah, wait, said his uncle placidly ; " I spoke too hastily. I see there is a tail to the 0, which had escaped my notice. It was a 9."

\es. sir, I did," said Fred, laughing. Please tell us how to do it."

"I wish for once you children would guess a [(lizzie yourselves, said Uncle Bob; "but I suppose you never will, so I'll tell you. It s really very simple when you know how. Well." lie continued, "after Ik line, is written down, and the sum of its digits suhtiacted, and a single figure crossed off, you have a- row of iiuures handed to you. You must mentally arid these ami sub.straet their sum from the next multiple of 9. Thai sounds complicated: but it is not at all. If the sum ot the figures given you adds up to £<>, the? next multiple of 9 is 27, and the number you're in search of iv -'I- 1; 1,.. row ol tissues adds up to 59, the number .'.truck out- was 6, because that added |«. 39 makes 45, which is (he next mujlip! ' of 9. Do you understand'.'" " \ e>. said Lucy, wrinkling Iter for-?-head : "you just add the figures given von. and sub.straet that sum from whatever cornet* next higher in your 'nine times' multiplication table."

lliat.s right." said her uncle, "and the only time the rule won't work is when tie: number crossed out is either a9or aO. A* you can see fur y<uir.-elv< ». if tic diuit!" added up to 45. you wouldn't know whether a 9 or ;i 0 had Ivt o ero- *e(| out, because either of those added to 45 would :t*^tilt in a multiple of 9." "Oh. said Fred, " that's why you made up that yarn about, the tail to the 0." "\es. raid Uncle bob, "and though you may work that little ru*e once, if you arc cornered a second time it is better to own tip frankly that it was either a 9 or a 0. and you don't know which. Never act as if yon were adding the figure:; up. The charm of all these tricks is to appear to be usintr a sort of elsirvoyanev. This impressed your audience more than a mere arithmetical calculation would.