this month, Stage 3 & 4

April 2000

 

Problems

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Pick

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

Investigate polygons with all the vertices on the lattice points of a grid. For each polygon, work out the area A, the number B of points on the boundary and the number of points (I) inside. . . .

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Read This Page

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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Clocks and Bases

Stage:4 Challenge Level:Challenge Level:1

Investigate and explain the link between how numbers are recorded in modulus arithmetic and the units digit when the number is written in a different number base. Here is an example of a few randomly. . . .

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By the Quad - Quick Solve

Stage:4 Challenge Level:Challenge Level:1

In the triangle ABC, P is a point on AB, Q is a point on AC and BQ meets CP at O. The areas of the triangles PBO, OBC and CQO are 8, 10 and 5. What is the area of the quadrilateral APOQ?

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Shaded Circles

Stage:4 Challenge Level:Challenge Level:1

If the area shaded yellow inside the outer circle equals the area in blue of the larger of the two internal circles, find the relationship between the diameters of the three circles.

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The Medieval Octagon

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

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

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Never Prime

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

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

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Secants

Stage:4 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

From a point P two lines are drawn cutting a circle at A, B, C and D. What can you discover about the lengths PA, PB, PC and PD? Prove your results.

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LOGO Challenge - Pentagram Pylons

Stage:3, 4 and 5 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?