A Very Special Ten-Digit Number
This puzzle was given to me by John H. Conway, and he heard it from someone else:
Find a ten-digit number with all distinct digits such that the string formed by the first k digits is divisible by k for any k ≤ 10.
Surprisingly, there is a unique solution to this puzzle. Can you find this very special ten-digit number?
For the contrast, consider ten-digit numbers with all distinct digits such that the string formed by the last k digits is divisible by k for any k ≤ 10. These numbers are not so special: there are 202 of them. My puzzle is: find the smallest not-so-special number.Share:
An Answer To “A Very Special Ten-Digit Number” | Finer Recliner:
[…] Khovanova poses an interesting math question on her blog: This puzzle was given to me by John H. Conway, and he heard it from someone […]4 September 2008, 7:50 am
Fun puzzle. Bit of reasoning deals with all but the div-by-7 case, and then used brute force trying all 8 possibilities.4 September 2008, 10:25 am
Has anyone found a way to reason thru to the solution without need for division in the div-by-7 test?
Took me about an hour of eliminating results based on divisibility rules here:5 September 2008, 7:26 am
I got 3816547290 for Conway’s puzzle.
For your puzzle, I had to write a computer program, and got 9123567480.
Thanks for the intriguing puzzle!
Walking Randomly » The 46th Carnival of Mathematics - the last one of 2008.:
[…] No Carnival is complete without a puzzle to solve and Tanya Khovanova gave us a great one back in […]29 December 2008, 2:42 pm
Tanya Khovanova’s Math Blog » Blog Archive » It Has Been Two Years:
[…] A Very Special Ten-Digit Number […]11 December 2009, 10:20 am