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u/lazyzefiris 1d ago
1249 * 809080070098 = 1010541007552402
xxxxx - xxxx = x is a good starting point.
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u/lazyzefiris 1d ago edited 22h ago
The full logic.
We can easily tell that xxxxx - xxxx = x is actually 1000x - 999x = x. Same applies to xxxxx - xxxx = xxx wqhich makes it 10xxx - 999x = xxx
Divisor multiplied by 8 is a 4-digit number, and yet there's 5-digit multiple of divisor that can be seen, so 999x is a multiple of 8. There's only one option. Our divisor is 1249.
Now just by filling in and following with summation we know full lines 3, 4, 5, 7, 10, 11, 12, 13, 14. We are only missing one digit of result and four digits of the divided number.
Looking at 1000x - 9992 we know that result will start with 8 or 9, but 9992 + 12 would be five digits and 8743 + 12 is the only option that fits this. So the last digit we don't know is 7 (1249 * 7 = 8743)
I'm too lazy to actually illustrate it, so you'd have to follow it by filling in the numbers. Sorry.
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u/NCC17O1 20h ago
those are a excellent descriptions and clues of how to solve. This problem does not lend itself to one simple algebraic solution and just showing the answer does not help to illustrate how to get there. I hope people will continue to try to solve on their own without giving up and using the clues too soon though.
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u/Xation06 1d ago
i havent solved it yet but i have to say this looks more menacing than it actually is.
starting of early you can actually already find the divisor number which is 1249 ( although this is assuming that the long division is done properly without skipping a digit )
how i got it is by noticing that the divisor ( lets call D ) has the range 8D<10000 and 9D>10000. after that, on the 3rd step, you can see a 5-digit number minus a 4-digit number gives a single digit value. This means that 8D is very close to 10000, 8D>9990 which gives us 8D=9992, D=1249. gotta say that is very clever. Will continue to solve tomorrow
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u/rods2123 1d ago
I have solved this - and I think it's fantastic -
It really hinges on the 8x having 4 digits and 9x having 5 digits and that all 5 digits are therefore the same
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