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### Schools Mathematics Grand Challenge

PROBLEM 13:

One year, 50,000 students do junior cert maths. Most are honest, but 1% try cheating. When the exams are marked, a special system is used to make a list of students who might have cheated. The system is good, but not perfect. It puts 99% of the cheaters on the list, but, by mistake, a third of a percent of honest students are also on the list.

What percentage of the students on the list actually tried cheating? Give your answer to the nearest percent.

PROBLEM 14:

A tortoise, a hare and a cheetah start to run on a circular track from the same point at the same time and run around the path in a clockwise direction. The tortoise runs at a constant speed of 1 lap per hour; the hare at a constant speed of 7 laps per hour; and the cheetah runs at a constant speed of 13 laps per hour. After how many minutes will all three animals again be at the same point on the track at the same time?

PROBLEM 15:

The picture below illustrates a magical trick - we can rearrange the same set of 4 pieces into two identical big triangles. However somehow during the rearrangement a gap appears!

Using maths we can figure out what is going on here. First, check out the Tip of the Week to find out what the Tan of an angle is. Then figure out 120*Tan(A)-120*Tan(B)? The result is the answer to this puzzle.

You should now understand why the trick works!!