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FLOUR 07/30/22 4:09:13 PM #1: |
How do you find the digit values of a, b, and c without using a calculator? --- OK, so what am I doing? Oh, I'm chasing this guy? No, he's chasing me... ... Copied to Clipboard!
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FL81 07/30/22 4:10:47 PM #2: |
multiply it out by hand --- Thanks to Proofpyros for the sig images https://i.imgur.com/Nv4Pi1v.jpg https://i.imgur.com/N43HJYv.jpg ... Copied to Clipboard!
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Tyranthraxus 07/30/22 4:13:03 PM #3: |
FLOUR posted... How do you find the digit values of a, b, and c without using a calculator?Use Google instead --- It says right here in Matthew 16:4 "Jesus doth not need a giant Mecha." https://i.imgur.com/dQgC4kv.jpg ... Copied to Clipboard!
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Ricemills 07/30/22 4:44:27 PM #4: |
does it even matter? --- You have the right to remain silent. Anything you posted will be misquoted, then be used against you. http://error1355.com/ce/Ricemills.html ... Copied to Clipboard!
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Aressar 07/30/22 4:46:23 PM #5: |
Just do a lucky guess. The odds you get it right are much, much higher than winning the lottery. --- One time, CE triggered me so hard with their objectively wrong opinions that I accidentally punched myself in the balls. ... Copied to Clipboard!
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Eviora 07/30/22 5:29:28 PM #7: |
Since 15! has three factors of 5, and more than 3 factors of 2, it's certainly a multiple of 1000. So c = 0. 15! is also a multiple of 9, and 1 + 3 + 0 + 7 + 6 + 7 + 4 + 3 + a + b + 0 + 0 + 0= 31 + a + b which must be a multiple of 9. So 31 + a + b = 36 or 45 (a + b can't be higher than 14 because a and b are integers from 0 to 9 and if a + b = 23 then we need a or b to be over 9.) So a + b = 5 or 14. 15! is a multiple of 11, so 1 - 3 + 0 -7 + 6 - 7 + 4 - 3 + a - b +0 - 0 +0 = -9 + a - b is a multiple of 11. Again, since a and b are integers from 0 to 9, the only conceivable values of - 9 + a - b are -11 and 0. Suppose - 9 + a - b = 0. Then a = b + 9. That can only be true if b = 0. But we don't have a fourth multiple of 5, so b can't be 0. Suppose - 9 + a - b = -11. Then a - b = -2 so a = b -2 so a+ b = 2b - 2. 2b - 2 must be even, so it can't be 5. So a + b = 14. Now 2b - 2 = 14 which makes b = 8 and a = 6. It probably would have been faster to just manually multiply. Just with basic algebra, this level of reasoning is possible for Eviora. What do you think? --- Cunning, cruel, and cuddly. ||| 3DS Friend Code: 2449-5292-9560 IGN: Amy ... Copied to Clipboard!
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SoIidLegacy 07/30/22 5:42:23 PM #8: |
Eviora posted... Since 15! has three factors of 5, and more than 3 factors of 2, it's certainly a multiple of 1000. So c = 0. Well, I said "brown"... --- The secrets of the ancient world have been unearthed. The shackles of false histories destroyed. Together we stand as the authors of destiny. ... Copied to Clipboard!
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Paragon21XX 07/30/22 5:44:44 PM #9: |
Start by finding the factors of 15! 2^11 * 3^6 * 5^3 * 7^2 * 11 * 13 I can guarantee c=0 because 2^3 * 5^3 = 1000 Removing those factors: 2^8 * 3^6 * 7^2 * 11 * 13 = 13076743ab a + b = 5 or 14 (1+3+7+6+7+4+3=31) as the entire number must be divisible by 9 (3^2), and the digits of any number divisible by 9 will add up to a multiple of 9 ab is also divisible by 4 as 2^2 is one of the factors, so we need a 2 digit number divisible by 4 whose digits add up to 5 or 14. The only 2 number who fit that bill are a=6 and b=8 as 68 is divisible by 4 but not 86. Eviora posted... Just with basic algebra, this level of reasoning is possible for Eviora. What do you think?Overcomplicated solution. I give it 80/100. --- Politicians are the weeds of the galaxy. ... Copied to Clipboard!
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Eviora 07/30/22 5:58:43 PM #10: |
Fair. However, your solution is incomplete since 32 is a 2 digit number divisible by 4 whose digits add up to 5. You did not go to the trouble of ruling it out. --- Cunning, cruel, and cuddly. ||| 3DS Friend Code: 2449-5292-9560 IGN: Amy ... Copied to Clipboard!
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Paragon21XX 07/30/22 6:05:39 PM #11: |
Eviora posted... Fair. However, your solution is incomplete since 32 is a 2 digit number divisible by 4 whose digits add up to 5. You did not go to the trouble of ruling it out.Okay, 332 is not divisible by 8 but 368 is. Happy now? --- Politicians are the weeds of the galaxy. ... Copied to Clipboard!
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Eviora 07/30/22 6:09:14 PM #12: |
That's a definite improvement. A proper proof would have gone through the list one by one to find then eliminate all the other possible two digit numbers with those properties, though. =p --- Cunning, cruel, and cuddly. ||| 3DS Friend Code: 2449-5292-9560 IGN: Amy ... Copied to Clipboard!
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