Digital Puzzles 33five and the smallest square number with five similar digits at the end might
be 24677777. But this is certainly not a square number. Of course, 0 is not to
be regarded as a digit.- THE TWO ADDITIONS
Can you arrange the following figures in two groups of four figures each so
that each group shall add to the same sum?12345 789
If you were allowed to reverse the 9 so as to change it into the missing 6 it
would be very easy. For example, 1,2,7,8 and 3, 4,5,6 add up to 18 in both
cases. But you are not allowed to make any such reversal.
- THE REPEATED QUARTETTE
If we multiply 64253 by 365 we get the product 23452345, where the first
four figures are repeated. What is the largest number that we can multiply by
365 in order to produce a similar product of eight figures with the first four
figures repeated in the same order? There is no objection to a repetition of
figures-that is, the four that are repeated need not be all different, as in the
case shown.
- EASY DIVISION
To divide the number 8,1 0 1,265,822,784 by 8, all we need do is to
transfer the 8 from the beginning to the end! Can you find a number begin-
ning with 7 that can be divided by 7 in the same simple manner?- A MISUNDERSTANDING
An American correspondent asks me to find a number composed of any
number of digits that may be correctly divided by 2 by simply transferring the
last figure to the beginning. He has apparently come across our last puzzle with
the conditions wrongly stated. If you are to transfer the first figure to the end
it is solved by 3 I 5 7 8 9 4 7 3 6 84 2 I 0 5 2 6, and a solution may easily be
found from this with any given figure at the beginning. But if the figure is to
be moved from the end to the beginning, there is no possible solution for the
divisor 2. But there is a solution for the divisor 3. Can you find it?