Question

I am a number between 7 000 000 and 8 000 000 all my digits are odd all the digits in my thousands period are the same all the digits in my units period are the same the sum of my digits is 31 what number am i ?

Answer 1

Any of 7,111,777 or 7,333,555 or 7,555,333 or 7,777,111.

Explanation:

The first digit must be 7. The sum of the unknown digits is then 31-7 = 24. Since this represents 3 pairs of digits (a thousands period digit and a units period digit), each pair must total 24/3 = 8.

There are two ways that odd numbers can total 8: 1+7 = 3+5 = 8. Since there is no restriction on the digits other than they must be the same in any period and they must be odd, there are 4 ways the 2 pairs of digits can be arranged into a number:

• 7,111,777
• 7,333,555
• 7,555,333
• 7,777,111