# Sunday Times Teaser 2645 – One Square

*by Andrew Skidmore*

After consistently using different letters for different digits I have found that (FIVE – FOUR) squared is equal to ONE.

You could work out the numeric value of FIVE if you knew whether THREE is divisible by 3 and whether FOUR is divisible by 4.

What number does FIVE represent?

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There is an ambiguity in the puzzle since it is unclear whether FIVE has to be larger than FOUR. The following program allows either choice to be made.

(FIVE-FOUR)^2=ONE=196 , 256 , 361 , 576 , 625 , 841 , 961

(FIVE-FOUR)= 14 , 16 , 19 , 24 , 25 , 29 , 31

E-R=1-0 , 1-2 , 5-0 , 6-0 , 6-2 giving us the following solutions:

ONE FOUR FIVE THREE

361 5382 5401 79211/97211

361 7382 7401 59211/95211

361 9382 9401 57211/75211

625 3690 3715 48055/84055

625 4690 4715 38055/83055

625 8390 8415 47055/74055

841 3872 3901 56211/65211

841 5872 5901 36211/63211

841 6872 6901 35211/53211

one of which gives us the solution.