Logic and Algorithms - March 2008, Stage 4&5

Problems

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Simple Counting Machine

Stage: 3 and 4 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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Circuit Maker

Stage: 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?

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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?