Brain Teasers
The Mystery of Number 11
Can you find the largest number possible containing any of 9 of 10 digits, considering 0 also a number, that is divisible by 11 without a remainder?
(Note: each number may appear only one time.)
(Note: each number may appear only one time.)
Answer
987652413, is the highest number possible containing any of 9 of 10 digits and is divisible by 11 without a remainder.Hide Answer Show Answer
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Comments
Thank you - very nice, the algorithm to solve this was a delight to discover. Well done.
If you start with that number and continue to add 11 to it, you can get even larger numbers. IN fact, if you add 110000000 to it, you'll get 1097652413, which is a 10-digit number divisible by 11, and you can keep adding 11's to that to continue to get numbers divisible by 11.
The teaser is not very well worded, but I think that it means find the largest 9-digit number, with no repeated digit, which is divisible by 11. If the teaser is understood that way, the solution given is correct.
Easy. For number to be divisible by 11, the sum of even digits of the number must be ether equal to sum of odd digits of the number, or be more or less then the sum of odd digits by a number divisible by 11.
havent peek at ur answer yet, but 1st commentor told me u explained ur derivation. i got mine by putting the 98765 for tha 1st 5 digits and find the remaining 4(2 pairs with their sums differ by 4, the set with lesser sum to be put at the even placing from the rear, and in descending order for both pairs) by trial(s) n error(s). i dont think my way's systematic enuff so thank you in advance 4 explaining urs.
are you sure that's is the largest number??
based on my calculations, the biggest number i've got that is divisible by 11 is 9870654321.. which, if divided by eleven is 89733211.. check it out..
based on my calculations, the biggest number i've got that is divisible by 11 is 9870654321.. which, if divided by eleven is 89733211.. check it out..
opps... sorry i didn't read the 9 of 10.. my mistake..
Thanks for your puzzle.
I managed to solve it with glpsol (a free linear and mixed integer programming solver, available for most platforms). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it.
http://pastebin.com/YR6wn9v8
I managed to solve it with glpsol (a free linear and mixed integer programming solver, available for most platforms). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it.
http://pastebin.com/YR6wn9v8
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