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450.

(Note: "x" below signifies that this digit is temporarily being ignored)

This is true for:

10x1

11x2

12x3

13x4

14x5

15x6

16x7

17x8

18x9

So for the first eligible 1000 numbers there are 9 (when we disregard the third digit).

For the next 1000 (that is 2000 to 2999) there will be 8 (it is one less because the first digit is 2 and not 1)

This pattern will continue all the way through the 4 digit numbers, so that our answer is:

9+8+7+6+5+4+3+2+1 = 45.

However as "x" above (that we temporarily ignored) can be any digit we have to multiply this by 10 (as there are 10 digits). Therefore the answer will be 450!

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13y ago

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Q: How many 4-digit numbers have the last digit equal to the sum of the first two digits?
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