Anonymous asked:

A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules: 1. X= W+Y+Z 2. W=Y+1 3. Z=W-5 What is the four-digit integer?

Think through this one logically. Here’s what you know right away:

X is the biggest digit.
Z is the smallest digit. 

So try X = 9 and Z = 0 and see how that works:

If X = 9, and Z = 0, then W = 5 and Y = 4. 

WXYZ = 5940.

There are other ways to think about this, too. You could, for example, notice that W and Y are 1 apart, and W is at least 5, so the only way W, Y, and Z could add up to a number small enough to be a single digit (X) is if they’re 5, 4, and 0.

Basically, when you’re confronted with something like this where there doesn’t seem to be an obvious entry point, just jump in somewhere and see where it takes you. Worst case scenario, it gets you nowhere. But even then, you’re no worse off than if you just sat there staring at the problem instead of writing something down.

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