Logic and Algorithms - March 2008, Stage 2&3

Problems

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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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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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Circuit Maker

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

Investigate how logic gates work in circuits.

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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?