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Schools Mathematics Grand Challenge

Final Week's Puzzles

These are the final puzzles. We will be announcing the winners shortly after the final answers are submitted. We will also be making available the solutions to the final problems.

Problem 19:

John was born in the 20th century. On one of John's birthdays the age he turned was equal to the sum of the 4 digits in the year of that birthday and also equal to the sum of the 4 digits in the year he was born. What age did John turn on this birthday?

Problem 20:

What remainder do you get when you divide 10^(1,000,001) - 10^(1,000,000) by 11? So we want the remainder when you divide (10 to the power of 1,000,001) minus (10 to the power of 1,000,000) by 11. Your answer should be a whole number between 0 and 10.

HINT: An old tip of the week might be useful.


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Hamilton Institute - National University of Ireland Maynooth - Co. Kildare - Ireland Tel. + 353 (0) 17086100 - Fax. +353 (0) 17086269 - email