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### Schools Mathematics Grand Challenge

Week six's Puzzles

Problem 11:

There is exactly one three digit positive whole number (so a number between 100 and 999) with the following properties:

If you subtract 11 from it, the answer is divisible by 11;
If you subtract 10 from it, the answer is divisible by 10;
If you subtract 9 from it, the answer is divisible by 9.

What is the number?

Problem 12:

There are 70 students in a year, 36 girls and 34 boys. At the end of the school year, the students have a choice of two places to go on their school trip: either Galway or Cork. All of the students go on the trip with 25 students going to Galway, and the other 45 going to Cork. How many more girls went to Cork than boys went to Galway?

How many more girls went to Cork than boys went to Galway?

(We want the difference between the number of girls who went to Cork and the number of boys who went to Galway)