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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