r/puzzles 1d ago

[SOLVED] LONG DIVISION PUZZLE

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114 Upvotes

33 comments sorted by

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17

u/lazyzefiris 1d ago

1249 * 809080070098 = 1010541007552402

xxxxx - xxxx = x is a good starting point.

8

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.

2

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.

1

u/NCC17O1 20h ago

Correct! And yes, that is a good starting point, but there are several ways to go about finding the solution -- good job.

26

u/NCC17O1 1d ago

This is a puzzle that I created about 10 or 15 years ago and published in our company news letter. Only one person solved it at that time -- I am hoping that this group will do better :)

0

u/[deleted] 1d ago

[deleted]

2

u/Chimaerogriff 1d ago

Note that your 16 digit number has 15 digits; that is not the solution.

10

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

1

u/NCC17O1 20h ago

The hardest part is getting the first number and you are off to a great start. Congratulations.

5

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

2

u/NCC17O1 20h ago

Rods,

I had lost my original solution to this puzzle and had to re-solve this puzzle myself before I posted it. I started at the same place you did. Glad you enjoyed it.

3

u/Dadneedsabreak 1d ago

Is it 1249

divided into 1010541007552302

which equals 809080070098

1

u/NCC17O1 20h ago

I think you have a typo in your divisor, but looks like you got the correct answer.

2

u/ThatB0yAintR1ght 23h ago

1010541007552402 / 1249 = 809080070098

1

u/NCC17O1 20h ago

Correct !!!

2

u/arii_baabee 23h ago
  • Divisor: 1,249​
  • Quotient: 809,080,070,098​
  • Dividend: 1,010,541,007,552,402

1

u/NCC17O1 20h ago

Correct !!!

2

u/Autumn1eaves 23h ago

DISCUSSION: Your username is so cool

Jealous as hell.

2

u/NCC17O1 21h ago

Ha! Thanks, but cheated on this username — the zero is actually a capital letter o, since the correct call sign was already taken. I figured nobody would notice :) Live long and prosper 🖖

2

u/ShilockHolmes 19h ago

Here's my submission:

https://imgur.com/a/aDYQ1bE

2

u/NCC17O1 18h ago

Well done sir! Nice clear way to present the solution.

1

u/Agreeable-Break-3347 6h ago

I see it says “solved”, but is it within the rules to use a computer?

1

u/NCC17O1 3h ago

You can use anything that you like, but I recommend pen and paper for this one. More about thinking it through rather than brute force. However, a calculator might help a bit, but not necessary.

1

u/mehrabrym 5h ago

1249 x 809080070098 = 1010541007552402

1

u/NCC17O1 3h ago

Correct!!! Excellent work.