Logic and Algorithms - April 2008, All Stages

Problems

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One of Thirty-six

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the chosen number from the grid using the clues?

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A Bag of Marbles

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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What Do You Need?

Stage: 2 Challenge Level: Challenge Level:1

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Cows and Sheep

Stage: 2 Challenge Level: Challenge Level:1

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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Shaping Up

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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How Much Did it Cost?

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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Rabbits in the Pen

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Tessellation Interactivity

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

An environment that enables you to investigate tessellations of regular polygons

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Flow Chart

Stage: 3 Challenge Level: Challenge Level:1

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

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Simple Counting Machine

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

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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Crossing the Bridge

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

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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Coins

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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Balance Power

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

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

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Peaches in General

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

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.

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Zeller's Birthday

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

What day of the week were you born on? Do you know? Here's a way to find out.

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Unusual Long Division - Square Roots Before Calculators

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

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

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Procedure Solver

Stage: 5 Challenge Level: Challenge Level:1

Can you think like a computer and work out what this flow diagram does?

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Adding Machine

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you set the logic gates so that this machine can decide how many bulbs have been switched on?

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Circular Circuitry

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What will happen when you switch on these circular circuits?