Make a list of all 120 five-digit numbers created by permuting the digits 1,2,3,4,5.
Consider it as a set of numbers in base-10 system, ranging from 12345 to 54321.

Show that it is possible to partition this set into 2 subsets possessing equal sums of squares of their respective members.

bonus question: Is the result dependent of the base we choose?

DIVIDE THE SET OF 120 POSSIBLE COMBINATIONS INTO TWO SUBSETS OF 60.
In the 1st subset a appears before b , like abcde, dacbe.
In the 2nd b appears before a , like bacde, dbcae.
Clearly the sums will be equal,independent of base and of the power (squares,cubes or else)we chose.

Comments: (
You must be logged in to post comments.)