What's the opposite?

Logic Level 3

S P E N D − L E S S M O N E Y \begin{array} { l l l l l } & S & P & E & N & D \\ - & & L & E & S & S \\ \hline & M & O & N & E & Y \\ \end{array}

The above shows a cryptogram, with each letter representing a distinct single digit non-negative integer with S , L , M > 0 S,L,M > 0 . What is the number of all possible distinct solution(s) for this cryptogram?

Inspiration .

Infinitely many solutions 2 1 Some integer between 3 and 30 inclusive 0

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Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Thomas Burns
Dec 14, 2015

Notice that N + E = E. Therefore N is 0 or 9. If N is 0, then E + S must be 10, but since this carries N=0 is not possible. If N is 9, then E + S must carry and therefore by 19, but since the only digit combination is 8 and 9, and 9 is already taken, N cannot be 9 either. This means there are no solutions.

8 Helpful 2 Interesting 0 Brilliant 0 Confused

Right. Thank you.

Chung Kevin - 5 years, 6 months ago

That's what i did!

Kristin Ross - 1 year, 8 months ago
John Hopkins
Jun 27, 2015

Almost certainly not a complete solution, but...

E-E = N, so N = 0.

N - S = E, therefore, 0 - S = E.

Both E and S are positive numbers, therefore there cannot be a solution.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

it clearly indicates that N - S = 0 - S, therefore N = S - S, N = 0

Razor M - 1 year, 9 months ago

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