Volume 5
, Issue 2


The playing of games has its origins in antiquity - the ancient Romans, Greeks and Chinese all played games of varying degrees of difficulty.

J121 The numbers $a,b,c,d$ and $e$ are consecutive integers, each smaller than $10,000$.

J111 The integer $M$ consists of 100 threes and the integer $N$ consists of 100 sixes. What digit occurs in the product $MN$?

$a,b$ are integers such that $a+b$ and $a^2 +b^2$ are both divisible by $7$. Prove that both $a$ and $b$ are both divisible by $7$.