Digital Puzzles 41first total, 657, and the second, 819, is the same as the difference between
the second, 819, and the third, 981-that is, 162.
Can you form eight such squares, everyone containing the nine digits, so
that the common difference between the eight totals is throughout the same?
Of course it will not be 162.- THE NINE DIGITS
It will be found that 32,547,891 multiplied by 6 (thus using all the nine digits
once, and once only) gives the product 195,287,346 (also containing all the
nine digits once, and once only). Can you find another number to be multi-
plied by 6 under the same conditions? Remember that the nine digits must
appear once, and once only, in the numbers multiplied and in the product.- EXPRESSING TWENTY-FOUR
In a book published in America was the following: "Write 24 with three
equal digits, none of which is 8. (There are two solutions to this problem.)"
The answers given are 22 + 2 = 24, and 33 - 3 = 24. Readers familiar
with the old "Four Fours" puzzle, and others of the same class, will ask why
there are supposed to be only these solutions. With which of the remaining
digits is a solution equally possible?- THE NINE BARRELS
In how many different ways may
these nine barrels be arranged in three
tiers of three so that no barrel shall
have a smaller number than its own
below it or to the right of it? The first
correct arrangement that will occur
to you is I 23 at the top, then 4 5 6 in
the second row, and 789 at the bot-
tom, and my sketch gives a second
arrangement. How many are there
altogether?