To Guess The Result Of A Sum

Source: What Shall We Do Now?: Five Hundred Games And Pastimes
Category: THINKING, GUESSING, AND ACTING GAMES



Another trick. Tell the person to think of a number, to double it, add
6 to it, halve it and take away the number first thought of. When this
has been done you tell him that 3 remains. If these directions are
followed 3 must always remain. Let us take 7 and 1 as examples. Thus 7
doubled is 14; add 6 and it is 20; halved, it is 10; and if the number
first thought of--7--is subtracted, 3 remains. Again, 1 doubled is 2;
6 added makes 8; 8 halved is 4, and 1 from 4 leaves 3.

A more bewildering puzzle is this. Tell as many persons as like to, to
think of some number less than 1,000, in which the last figure is
smaller than the first. Thus 998 might be thought of, but not 999, and
not 347. The amount being chosen and written down, you tell each
person to reverse the digits; so that the units come under the
hundreds, the tens under the tens, and the hundreds under the units.
Then tell them to subtract, to reverse again, and add; remarking to
each one that you know what the answer will be. It will always be
1089. Let us suppose that three players choose numbers, one being 998,
one 500, and one 321. Each sets them on paper, reverses the figures,
and subtracts. Thus:--

998 500 321
899 005 123
--- --- ---
099 495 198

The figures are then reversed and added. Thus:--

099 495 198
990 594 891
---- ---- ----
1089 1089 1089

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