Mathematical_Recreations-Kraitchik-2e

Numerical Pastimes 57
sponding to the presence or absence of the number in the
respective columns.
Mr. R. V. Heath had the idea of replacing the powers of
2 by colors. He writes the numbers in the first column on a
red sheet, those in the second on a white sheet, those in the
third on a blue sheet, and so on. In forming the nurr .. ber we
count 1 for the red, 2 for the white, 4 for the blue, and so on.
Mr. Perelman devised a scheme by which an automaton
could be made to give the answer. The sets of numbers are
written on cards weighing 1 unit, 2 units, 4 units, and so on,
respectively. Then we have only to put the cards on which
the number appears in the pan of an automatic weighing
machine in order to read off the number.
6. There are similar methods which use the ternary scale
of notation. For example, we may list in the first and second
III II I
5 2 1
6 3 2*
7 4 4
18 9 6 3 2 1 8 5* 5*
--------I----
18 9 6 3 2 1
9 6* 7
10 7* 8*
19 10 7 4 5 4
20 11 8 5 8 7 11 11 10
12 12 11*
21 12 15 12 11 10
13 13 13
22 13 16 13 14 13
14* 14* 14*
23 14 17 14 17 16
15* 15* 16
24 15 24 21 20 19 16* 16* 17*
25 16 25 22 23 22
26 17 26 23 26 25
17* 20 19
18* 21 20*
19* 22 22
20* 23* 23*
21* 24* 25
22* 25* 26*