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The Liars' Rail

Math brain teasers require computations to solve.


Puzzle ID:#47469
Fun:*** (2.5)
Difficulty:*** (2.77)
Submitted By:dalfamnestAnz******




The people of Olde Mathville had unique ways of punishing wayward citizens. For example, those convicted of crimes of dishonesty were chained to the Liars' Rail until they solved a number of puzzles.

One such puzzle has been recently discovered!

In the multiplication below, each letter - L, I, A, R, and S - takes the place of a different digit. Find the digits to make the multiplication true.

x S

or: L I A R x S = R A I L

Open Calculator


The product of S x L must be less than 10. Combining that with the need for S x R to end in L limits the possibilities quickly.

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Jul 18, 2010

Nicely done, but pseudo-unique; too much like 50 others.
Jul 21, 2010


This comment is not meant to be insulting, if you know what I mean you know what i mean.
Aug 16, 2010

Excellent puzzle!
Oct 23, 2012

A really tough one and luckily I was able to solve it, with reasoning similar to that of the creator of this problem. Obviously S cannot be 1, and L cannot be 5,6,7,8 or 9. Hence L can only be 0,1,2,3 or 4. By trying out each of these possible values for L and eliminating them one by one, taking different values for S, I got the answer LIAR=2178 and S=4.
I started with L=4 and so took time to arrive at the solution. Still, I had to eliminate any other possible solution by trying out all values for L.
A great puzzle. Thanks for making me think logically.

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