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"Truth is always strange,..."
(9048'3 256)
```
W O R D
* L I S T
x x x x D
x x x R
x x x x O
x x x x W
x x x x x x x x```

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 re: Hand solution Comment 3 of 3 |
(In reply to Hand solution by Jer)

Well, it only took me 26 months to notice and correct Jer's hand solution (sorry, Jer).

I agree with the first step: "There are 8 unique letters in the alphametric and there is no 1 or 7 in (9048'3 256) this indicates none of the letters is a 1 or 7."

But the analysis goes wrong at step 2.

The problem with it is that it seems to be saying that
D*T = xD
R*T = xR
O*T = xO
W*T = xW

It then concludes that T must therefore be 6.

It turns out that T does equal 6, but the reasoning is wrong, as this is not the way that partial products work.

Instead, what we know is that:

T*D = xD
S*D = xR
I*D = xO
L*D = xW

D clearly cannot be 5 or 0, since the partial products end in 4 different digits.
Therefore, from T*D = D, we can conclude that D is even and T = 6.
And because D is even, it follows that R, O and W are also even.
So the top row has the digits 0, 2, 4 and 8 in some order.

And now the analysis is back on track!

 Posted by Steve Herman on 2014-06-19 16:08:17

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