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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

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Have You Got It?

Can you explain the strategy for winning this game with any target?

Expanding Zeros

Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
See all short problems arranged by curriculum topic in the short problems collection

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: 200,007
B: 20,000,007
C: 2,000,000,007
D: 200,000,000,007
E: 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.