"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

(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!