this month, Stage 3 & 4

March 2000

 

Problems

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Base Puzzle

Stage:3 Challenge Level:Challenge Level:1

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.

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Clock Squares

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

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

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Happy Octopus

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

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.

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Soma - So Good

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

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

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Route to Root

Stage:4 Challenge Level:Challenge Level:1

A sequence of numbers x1, x2, x3, ... starts with x1 = 2, and, if you know any term xn, you can find the next term xn+1 using the formula: xn+1 = (xn + 3/xn)/2 . Calculate the first six terms of. . . .

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First Forward Into Logo 10

Stage:3, 4 and 5 Challenge Level:Challenge Level:1

What happens when a procedure calls itself?

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Napkin

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

A square of paper is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed (where there is a single thickness of the paper).

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Major Trapezium

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

A small circle in a square in a big circle in a trapezium. Using the measurements and clue given, find the area of the trapezium.

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Cushion Ball

Stage:4 and 5 Challenge Level:Challenge Level:1

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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Pentagon from 1926

Stage:4 and 5 Challenge Level:Challenge Level:2Challenge Level:2

Find the vertices of a pentagon given the midpoints of its sides.

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Triple Decker Sandwich

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

There are 150 8-sandwiches like 6 1 5 1 8 4 7 6 5 2 4 3 2 8 7 3 with 1 number between the 1's, 2 between the 2's etc. Can you find sandwiches where each digit occurs three times rather than twice?