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Puzzle - Answer

In the following sum the digits 0 to 9 have all been used, O = Odd, E = Even, zero is even and the top row's digits add to 9. Can you determine each digit?

?

 [Ref: ZVZB] © Kevin Stone

Answer:

?


Remembering that:

   E + E = E
   O + O = E
   E + O = O

To discuss individual letters it's easiest to represent the sum as:

   A B C
   D E F +
--------
 G H I J

The largest values for A and D are 6 and 8, which makes G = 1.

Since column 2 is E + O = O there can be no carry from column 1 (since E + O + 1 is always even). Therefore C and F are 3 and 5 (but we don't yet know which is which), therefore J = 8.

There can't be a carry from column 2 (as A + D is even) therefore E can't be 9 as this would force a carry.

Therefore I = 9. Hence B can't be 0. Therefore H = 0.

The last remaining odd number makes E = 7. Making B = 2.

Therefore A and D are 4 and 6 (but we don't yet know which is which).

Since the top row's digits have to add to 9 the top number must be 423.

This makes the sum 423 + 675 = 1098. QED.

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