## 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:  1. 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 2. 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 3. 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: 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\*909 → yes 4. 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 5. 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! *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ### The next contest starts tomorrow. Don't miss it!
author | quantumdeveloper |
---|---|
permlink | math-contest-13-results-and-solution |
category | puzzle |
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voter | weight | wgt% | rshares | pct | time |
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anomaly | 0 | 123,416,109 | 1% | ||
ejemai | 0 | 3,442,121,495 | 100% | ||
farizal | 0 | 5,044,722,887 | 100% | ||
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golddeck | 0 | 2,939,244,421 | 100% | ||
driveforkids | 0 | 37,263,119,263 | 40% | ||
contrabourdon | 0 | 56,461,303,932 | 10% | ||
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quantumdeveloper | 0 | 3,706,003,680 | 100% | ||
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ggvoter | 0 | 660,883,026 | 75% | ||
curation.stem | 0 | 806,623,401 | 75% |
Thanks!
author | golddeck | ||||||
---|---|---|---|---|---|---|---|
permlink | re-quantumdeveloper-2019930t83735588z | ||||||
category | puzzle | ||||||
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---|---|---|---|---|---|
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