Interesting integers

Computer Science Level 4

A positive integer ends in a 9. When the 9 is moved to the front of the integer, the integer is exactly nine times the original integer. What are the last 33 digits of the integer?


The answer is 561797752808988764044943820224719.

Freddie Hand by Freddie Hand , 18, United Kingdom

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1 solution

Abdelhamid Saadi
Feb 14, 2017

Minimum such number is 10112359550561797752808988764044943820224719 10112359550561797752808988764044943820224719

Others numbers are obtained by repeating this many times.

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Using algebra, we represent the given conditions as 9X = 9*10^N + (x-9)/10.

Checking for multiple N starting from 34, we find N=43 to give an integer solution, then get the last digits. (I used wolfram alpha for the computations)

Alex Li - 3 years, 12 months ago

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