*W*,

*X*,

*Y*, and

*Z*all have to be integers between 0 and 9 for this to work. Let's look at the rules (and what they tell us):

*X*=

*W*+

*Y*+

*Z*-- This tells us

*X*has to be the biggest number.

*W*=

*Y*+ 1 -- This one's obvious:

*W*is bigger than

*Y*, but only by 1.

*Z*=

*W*- 5 -- This one tells us a LOT, because the lowest

*Z*can be is 0.

Let's start putting things together. Because of the third rule, we know

*W*is either 5, 6, 7, 8, or 9 (otherwise

*Z*would be negative). But it can't be too big, because the second rule says

*W*is only 1 bigger than

*Y*, and the first rule says

*X*equals the sum of all the other letters. Confused yet? If so, do a little guess and check with possibilities for

*W*to see what happens to the other values.

Here's what I'm coming up with:

**W****= 5**. Why? Because if it was any bigger, like 6,

*Y*would also be bigger, like 5 ( because of the second rule), so

*X*would be bigger than 9 (by the first rule), which can't happen. Once you've got

*W*, the rest sorta fall into place.

**Y****= 4**. Why? Because

*W*= 5 and the second rule tells us

*Y*is one less.

**Z****= 0**. Why? Because

*W*= 5 and the second rule tells us

*W*- 5 =

*Z*.

**. Why? Because the first rule tells us that**

*X*= 9*X*is the sum of all the others and 5 + 4 + 0 = 9

**Our**

*WXYZ*number is 5940.
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