A fifty digit positive integer satisfies all these given conditions:
- The number is constituted entirely by the digit 1 with the exception of the units digit.
- The number is divisible by 53.
Determine the units digit.
Extra Challenge: Solve this puzzle without using a computer-assisted method.
To tackle this I crossed my fingers and hoped 53 would divide into a number with a shorter number of 1's. Using short division* I hit the jackpot at 13.
1111111111111/53 = 2096430587
50 = 3*13 + 11 so we need the 10th remainder which is 31.
311 isn't divisible by 53 being a bit short of 6 (only 5 as seen in the short division quotient. It's the 10th digit if you count two leading zeros)
311-5*53=46 so we need to add 53-46=7 to our number. Hence the units digit is 8.
1111111118/53=20964306
*Short division is a quicker alternative to long division. https://www.yout_ube.com/watch?v=SLze82Zcc4Y
|
|
Posted by Jer
on 2022-05-04 09:25:23 |
Short division
