So Many Sums
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
Age
11 to 14
Challenge level
Problem
In this addition, each letter stands for a different digit, with $S$ standing for 3.
What is the value of $Y\times O$?
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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: 42
S is 3
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The letters are all different so M is not 3, so 1 has been carried and M is 2
A and U are different so 1 has been carried
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A + 1 makes 1 be carried into the last column,
so A + 1 = 10 and A = 9
So U = 0
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or N = 8 with 1 being carried
N cannot be 9 because 9 is taken
N = 8 and 1 was carried
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O + Y = 13
4 + 9 = 13 but 9 is taken
5 + 8 = 13 but 8 is taken
6 + 7 = 13
O and Y are 6 and 7 so O$\times$Y = 42