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## 'Carry Over' printed from http://nrich.maths.org/

$UK$ means $10U + K$ and $SMC$ means $100S + 10M + C$, so we have
$$10U+K+4=100S+10M+C$$ The left hand side is at most $$ 10 \times 9
+ 8 + 4 = 102$$ so $$100S+10M+C \leq 102$$ Therefore $S \leq 1$, so
$S=1$ (since it can't be zero). So $$10M+C \leq2$$ So $M=0$

$M$ has the lowest value.

*This problem is taken from the UKMT Mathematical Challenges.*