MATHEMATICAL RECREATIONS 201

Radix 5. 43 31

347 g
04 13
40 31
“ 4
Radix f. 31 0936 TS

13 012 2369 14325

—_— —_— ——

18 198 6993 39996
81 801 3996 69993

—_———

99 1080 10989 109989

486. In a two or three figure number interchanging the first
and last digits is the same as reversing the order of all the
digits. But this is generally not so for a number of more than
three figures.

For such numbers, however, special rules can easily be workt
out for the result of an operation like that explaind above in
which we reverse the order of all the digits instead of merely
interchanging the first and last digits.

For example, in the decimal system, starting with a four
figure number abcd,

 

if @ > d and b > ¢, the result is 10890;
if @ > d and b < ¢, the result is 9999.

Starting with a five figure number abcde,

if a > eand b > d, the result is 109890
if a > eand b < d, the result is 99099,

Examples. 0831 8245 74612 51734
1389 5428 21647 43715

8442 2817 52965 08019
2448 7182 56925 91080

10890 9999 109890 99099