Problem 284

Steady Squares

The 3-digit number 376 in the decimal numbering system is an example
of numbers with the special property that its square ends with the same
digits: 376^{2} = 141376. Let's call a number with this property a steady square.

Steady squares can also be observed in other numbering systems. In
the base 14 numbering system, the 3-digit number c37 is also a steady
square: c37^{2} = aa0c37, and the sum of its digits is c+3+7=18
in the same numbering system. The letters a, b, c and d are used for the
10, 11, 12 and 13 digits respectively, in a manner similar to the
hexadecimal numbering system.

For 1 n 9, the sum of the digits of all the n-digit steady squares in the base 14 numbering system is 2d8 (582 decimal). Steady squares with leading 0's are not allowed.

Find the sum of the digits of all the n-digit steady squares in the base 14 numbering system for

1 n 10000 (decimal) and give your answer in the base 14 system using lower case letters where necessary.

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**