this month, Stage 2 & 3

December 2001

 

Problems

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Tetrafit

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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Jigsaw Pieces

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

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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World of Tan - Pentominoes

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

Can you fit the tangram pieces into the outlines of these people?

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Two By One

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

An activity making various patterns with 2 x 1 rectangular tiles.

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Rod Measures

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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Islamic Tiling

Stage:3 Challenge Level:Challenge Level:1

One rich source of tilings is to found in the mausoleums, mosques and minarets found throughout the Islamic world. Below are three particular favourites of mine. Study them carefully, locate the. . . .

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Cogs

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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Marvellous Matrix

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

Circle any number in the matrix, for example, 608 as below. Draw a line through all the squares that lie in the same row and column as your selected number. Circle another number which has not got. . . .

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Eminit

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

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?