this month, Stage 3 & 4

September 2001

 

Problems

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Adding All Nine

Stage:3 Challenge Level:Challenge Level:1

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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Chocolate Maths

Stage:3 Challenge Level:Challenge Level:1

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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Tetra Square

Stage:3 Challenge Level:Challenge Level:1

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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More Mathematical Mysteries

Stage:3 Challenge Level:Challenge Level:1

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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Hex

Stage:3 Challenge Level:Challenge Level:1

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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Overlaid

Stage:2, 3 and 4 Challenge Level:Challenge Level:1

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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One or Both

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

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

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American Billions

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

Find the ten digit number in which the number formed by the first two digits from the left is divisible by 2, the number formed by the first three digits from the left is divisible by 3...