Carry over
Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?
Age
11 to 14
Challenge level
Problem
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Each letter stands for a different digit, and S is non-zero.
Which letter has the lowest value?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: M has the lowest value
Working out the possibilities
UK + 4 is three digits long so UK = 96, 97, 98 or 99
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The only one with no repeats is 98 + 4 = 102
0 is the lowest, which is M.
Using algebra
$UK$ 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.