536 Puzzles and Curious Problems

254 Answers

64 (the cube of 4); 23, I 04 (the square of 152), where 23 + 04 = 27 (the cube
of3).

124. REVERSING THE DIGITS

989,010,989 multiplied by 123,456,789 produces 122,100,120,987,654,321,

where the last nine digits are in the reverse order.

125. DIGITAL PROGRESSION

The Professor's answer was:

297

291

237

231

564

564

564

564

831

837

891

897

where the common differences are respectively 267, 273, 327, and 333. He
pointed out that the three digits in the central number may be arranged
in any of the six possible ways, and a solution may be found.
[Victor Meally tells me that Victor Thebault, in Parmi les Nombres Curieux,
page 140, shows that there are 760 such progressions. In addition to 456 and
its permutations, the middle number may be any of the permutations of the
following four sets of three digits: 258,267,348 and 357.-M. G.]

126. FORMING WHOLE NUMBERS

If you multiply 6,666 by the sum of the four given digits you will get the
correct answer. As I, 2, 3, 4 sum to 10, then 6,666 multiplied by 10 gives us
66,660 as our answer. Taking all possible selections of four different digits, the
answer is 16,798,320, or 6,666 X 2,520.

127. SUMMING THE DIGITS

There are several ways of attacking this puzzle, and the answer is
201,599,999,798,400. The sum of the digits is 45 and

45 X 8! = 1,814,400

Now write down-