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Expanding Zeros

Age 11 to 14 Short Challenge Level:

The following sequence continues indefinitely:

27 = 3 x 3 x 3
207 = 3 x 3 x 23
2 007 = 3 x 3 x 223
20 007 = 3 x 3 x 2223.......

Which of the following integers is a multiple of 81?

a) 20 000 007
b) 2 000 000 007
c) 200 000 000 007
d) 20 000 000 000 007

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.