## Solution

The problem of this contest was a bit harder and I'm not overly surprised that nobody completely solved every task. I'll give here a short summary how you could have solved them:

- This can be done with the 1-digit sum:

123456789 → 1+2+3+4+5+6+7+8+9 = 45, 45 is divisible by 3 → yes

4327384926 → 48 → yes

7777777777 → 10*7 = 70 → no - For this you needed to apply the new concept of 2-digit sums:

308 → 3+08 = 11 → yes

453825 → 45+38+25 = 108 → no

187869 → 18+78+69 = 165 → yes - This was a bit more tricky, because you would need to either guess or find the concept asked in 5. to figure out which digit sum to use.

909*11 = 9999 = 10⁴ → you needed to use the 4-digit sum:*909 → yes

46385600 → 4638+5600 = 10238 Here it is not so obvious, so I repeat the digit sum: 1+0238 = 239 → no

36369999 → 3636+9999 = 13635 I repeat it again: 1+3635 = 3636 = 4\*909 → yes

4072320 → 407+2320 = 2727 = 3\ - a)

I thought this task would be the most easy.

You wouldn't even need to know anything about digit sums to solve this :P.

If you know a number is divisible by two factors which have no common prime factor, you also know that the number is also divisible by the product of those 2 factors:

3\*11 = 33 and 9\*11 = 99

Easy, right?

b)

This one could again only be solved with the knowledge of five.

You can check for all factors of 10³ - 1 = 999 with the 3-digit sum. Those factors are:

3, 9, 27, 37, 111, 333, 999 - With any n-digit sum you can check for all factors of 10^n -1

Why is that?

You might need to figure it out yourself in a future contest. Until then I will keep it.

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### What is your chance of winning:

`p(You Win) = 1/n`

, `n = number of entries`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### List of participants with their entries:

Name | solutions found | comment |
---|---|---|

@tonimontana | 2. 5. | 10 STEM for you! |

@mmunited | 1. 2. 3. | Although you didn't get the concept of 3., you got the right results → 7 STEM for you! |

@golddeck | 1. 2. (4.) | You got many errors in 4., but you also got a few correct things. So I'll give 1.25 STEM for that task. → 4.25 STEM for you! |

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

## Winner draw:

Congratulations @golddeck, you won 1 SBI!*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

## Comments 1

Thanks!