1985 OIM Problems/Problem 5
Problem
To each positive integer we assign an integer non-negative such that these conditions are satisfied:
(i)
(ii) , when the unit digit of is 3
(iii)
Find . Justify your answer.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
Using rule (i) and (iii): . Since we need to assign a non-negative integer, then
Using rule (i):
Using rule (iii) and (ii):
Since we need to assign a non-negative integer, then
Therefore,
~Tomas Diaz. ~orders@tomasdiaz.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.