June 2002, Stage 3&4

Problems

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Tiling Designs

Stage: 3 Challenge Level: Challenge Level:1

Try to reproduce these tilings with a LOGO procedure!

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Letter Land

Stage: 3 Challenge Level: Challenge Level:1

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

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Put Out the Flags

Stage: 3 Challenge Level: Challenge Level:1

Tim and Beth both have a string of flags. Use the percentages to find out who has the most flags.

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Power Crazy

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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Prime Magic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

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Look Before You Leap

Stage: 4 Challenge Level: Challenge Level:1

The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?

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Are You Kidding

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

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CD Heaven

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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Thank Your Lucky Stars

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .