536 Puzzles and Curious Problems

18144

18144

18144

18144

Answers 255

to nine places, add up and put 00 at the end, and there is the answer.

128. SQUARING THE DIGITS

In four moves 73,34,48,25, we can get 157,326,849, which is the square
of 12,543. But the correct solution is I 5, 84, 46, which gives us the number
523,814,769, the square of 22,887, which is in three moves only.

129. DIGITS AND SQUARES

(1) 1,026,753,849 (the square of 32,043); (2) 9,814,072,356 (the square of
99,066).

130. DIGITAL SQUARES

The only two solutions are 567, with its square, 321,489; and 854, with its

square, 729,316. We need only examine cases where the digits in the root

number sum to 9, 18, or 27; or 8, 17, or 26, and it can never be a lower sum

than 317 to form the necessary six figures.

131. FINDING A SQUARE

Taking the six numbers in their order, the sums of their digits are:

46 31 42 34 25 34

146 7 7 7

Again adding, where necessary, the digits until we reach a single figure, we
get the second row of numbers, which we call the digital roots. These may be
combined in different triplets in eight different ways:

146 147 167 177 467 477 677 777

2 3 5 6 8 9 2 3