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**tony123****Member**- Registered: 2007-08-03
- Posts: 197

How many five-digit numbers are there in which the sum of the digits equals the sum of the square of the digits?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

16.

Why did the vector cross the road?

It wanted to be normal.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Yes, 16 if the number starts with a 1, and can't start with a zero.

Since the square of all digits from 0 to 9 get larger or stay the same, then

you don't get any up/down canceling in the sum, so then you have to

settle on just using zeros and ones.

10000

11000

10100

10010

10001

11001

11010

11100

10011

10110

10101

10111

11110

11101

11011

11111

Yup, 16!!

**igloo** **myrtilles** **fourmis**

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