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## #1 2007-11-16 10:19:49

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

### How many

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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## #2 2007-11-16 11:50:34

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

### Re: How many

16.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2007-11-16 17:25:18

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

### Re: How many

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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