August 2002, Stage 3&4

Problems

Special Numbers

Stage: 3 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

And So on and So On

Stage: 3 Challenge Level:

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

Darts and Kites

Stage: 4 Challenge Level:

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

Archimedes and Numerical Roots

Stage: 4 Challenge Level:

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Card Game (a Simple Version of Clock Patience)

Stage: 4 Challenge Level:

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

August 2002, Stage 3&4

Problems

Special Numbers

Stage: 3 Challenge Level:

And So on and So On

Stage: 3 Challenge Level:

Darts and Kites

Stage: 4 Challenge Level:

Archimedes and Numerical Roots

Stage: 4 Challenge Level:

Card Game (a Simple Version of Clock Patience)

Stage: 4 Challenge Level:

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