# Logic and Algorithms - April 2008, All Stages

## Problems

### One of Thirty-six

##### Stage: 1 Challenge Level:

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

### A Bag of Marbles

##### Stage: 1 Challenge Level:

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

### What Do You Need?

##### Stage: 2 Challenge Level:

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?

### Cows and Sheep

##### Stage: 2 Challenge Level:

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

### Shaping Up

##### Stage: 2 Challenge Level:

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

### How Much Did it Cost?

##### Stage: 2 Challenge Level:

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

### Rabbits in the Pen

##### Stage: 2 Challenge Level:

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

### Tessellation Interactivity

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

An environment that enables you to investigate tessellations of regular polygons

### Flow Chart

##### Stage: 3 Challenge Level:

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

### Crossing the Bridge

##### Stage: 3 Challenge Level:

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

### Coins

##### Stage: 3 Challenge Level:

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

### Simple Counting Machine

##### Stage: 3 and 4 Challenge Level:

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?

### Balance Power

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

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?

### Peaches in General

##### Stage: 4 Challenge Level:

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

### Zeller's Birthday

##### Stage: 4 Challenge Level:

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

### Unusual Long Division - Square Roots Before Calculators

##### Stage: 4 Challenge Level:

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

### Procedure Solver

##### Stage: 5 Challenge Level:

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