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Today Puzzle #735

Puzzle No. 735 鈥� Friday 8 May 2020

In order to prevent the spread of COVID-19 our government has enforced a lockdown. Discover which digit each letter represents in the following equation:

SCHOOL
+ SHOPS
= CLOSED

Today’s #PuzzleForToday has been set by Dr Daniel Bearup, a Lecturer in Mathematics at the University of Kent

Click here for the answer

C and S are not 0 since they are at the beginning of the numbers. Neither is L, since that would imply D = S.
S is not equal to C so C+S must allow us to carry 1.
We can carry at most 1 so S+1 = C.
So 2S+1(+1) > 10 (L is not zero) which requires S is 5 or more and C is 6 or more.

If S = 5 and C = 6, then L = 1 or 2 and O = 2 or 7.
If L = 1 then D = 6. Not possible.
If L = 2 then D = 7.
If D = 7 then O = 2. Not possible.

If S = 6 and C = 7, then L = 3 or 4 and O = 3 or 8.
If O = 3 then 2 H = 3. Not possible.
If O = 8 then 2 H + 1 = 8. Not possible.

If S = 7 and C = 8, then L = 5 or 6 and O = 3 (or 8 but C = 8).
But O = 3 is not possible since 2H = O (and 3+3 doesn’t carry a 1).

If S = 8 and C = 9, then L = 7 (or 8 but S = 8) and O = 4 (or 9 but C = 9).
L = 7 gives us D = 5.
O = 4 gives us H = 2 and 4 + P + 1 = E (L + S carries 1). So P + 5 = E. But we have assigned 2, 4, 5, 7, 8, and 9, so P = 1 and E = 6 (the only remaining pair separated by 5).

If S = 9 then C = 10, not possible.

So C=9, D=5, E=6, H=2, L=7, O=4, P=1, S=8 is the only possible solution.

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