Digital Puzzles 39- DIGITS AND SQUARES
One of Rackbrane's little Christmas puzzles was this: (1) What is the
smallest square number, and (2) what is the largest square number that con-
tains all the ten digits (I to 9 and 0) once, and once only?- DIGITAL SQUARES
It will be found a very good puzzle to try to discover a number which, to-
gether with its square, shall contain all the nine digits once, and once only, the
zero disallowed. Thus, if the square of 378 happened to be 152,694, it would
be a perfect solution. But unfortunately the actual square is 142,884, which
gives us those two repeated 4's and 8's, and omits the 6, 5, and 9.
There are only two possible cases, and these may be discovered in about a
quarter of an hour if you proceed in the right way.- FINDING A SQUARE
Here are six numbers: 4,784,887,2,494,651,8,595,087, 1,385,287,9,042,451,
9,406,087. It is known that three of these numbers added together will form a
square. Which are they?
The reader will probably see no other course but rather laborious trial, and
yet the answer may be found directly by very simple arithmetic and without
any experimental extraction of a square root.
- JUGGLING WITH DIGITS
Arrange the ten digits in three arithmetical sums, employing three of the
four operations of addition, subtraction, multiplication, and division, and
using no signs except the ordinary ones implying those operations. Here is an
example to make it quite clear:
3 + 4 = 7; 9 - 8 = 1; 30 + 6 = 5.
But this is not correct, because 2 is omitted, and 3 is repeated.- EQUAL FRACTIONS
Can you construct three ordinary vulgar fractions (say, '12, Ih, or 114, or any-
thing up to ¥l inclusive) all of the same value, using in every group all the