Jam and Egg Sandwich
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Age
11 to 14
Challenge level
Problem
Each different letter in the multiplication below stands for a different digit. Identical letters stand for the same digit. Work out the value which each letter represents.
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: EGG = 288, JAM = 576 (A = 7, E = 2, G = 8, J = 5, M = 6)
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E$\times$E is less than 10, so E is 1, 2 or 3
EGG$\times$1 = EGG not JAM so E is 2 or 3
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But for E=3, J=3$\times$3=9 maximum, so there shouldn't be a carried digit, so E can't be 3
2$\times$G is at most 18 so the digit which is carried is 1, not 2
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