### 11687 - Digits

Posted:

**Wed Mar 26, 2014 1:45 pm**Here's some input / output that I found useful during testing / debugging.

What's not entirely clear to me is why the AC output for input "1" is "1". Shouldn't it be "2"?

Let x0 = 1. Now,
Let's see what happens when x0's not equal to 1 but is less than 10.

Assume x0 = 2. Now,
Input:
AC Output:

What's not entirely clear to me is why the AC output for input "1" is "1". Shouldn't it be "2"?

**Update:****juniorAw**, answered this question on uHunt and I'd like to share what I learned. Recall, from the problem statement thatCode: Select all

`x(i+1) = the number of digits in the decimal representation of xi `

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`x1 = x(0+1) = the number of digits in the decimal representation of x0 = 1. So, x0 = x1.`

Assume x0 = 2. Now,

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```
x1 = x(0+1) = the number of digits in the decimal representation of x0 = 1. So, x0 != x1.
x2 = x(1+1) = the number of digits in the decimal representation of x1 = 1. So, x1 = x2.
```

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```
1
2
3
4
5
6
7
8
9
43
674
8394394390224254424242342324
888888888888888888888888888888232323289238923892389238923892389238923892
999999999999999999999999999999999999999999999992392392392392392923923923923923923923923923923923923923923333333333333333333333
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999943535353535935999999999999999999999999999999999999999999993454353535354353593999
END
```

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```
1
2
2
2
2
2
2
2
2
3
3
4
4
4
4
```