# Inspirations from Easter Conferences - September 2006, All Stages

## Problems

##### Age 5 to 7 Challenge Level:

Sort the houses in my street into different groups. Can you do it in any other ways?

##### Age 5 to 7 Challenge Level:

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

##### Age 7 to 11 Challenge Level:

How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?

##### Age 7 to 11 Challenge Level:

Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?

##### Age 7 to 11 Challenge Level:

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

##### Age 11 to 14 Challenge Level:

In a certain community two thirds of the adult men are married to
three quarters of the adult women. How many adults would there be
in the smallest community of this type?

##### Age 11 to 14 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?

##### Age 11 to 14 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?

##### Age 11 to 16 Challenge Level:

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

##### Age 14 to 16 Challenge Level:

On a "move" a stone is removed from two of the circles and placed
in the third circle. Here are five of the ways that 27 stones could
be distributed.

##### Age 14 to 16 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.

##### Age 16 to 18 Challenge Level:

Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.

##### Age 16 to 18 Challenge Level:

A spiropath is a sequence of connected line segments end to end
taking different directions. The same spiropath is iterated. When
does it cycle and when does it go on indefinitely?

##### Age 16 to 18 Challenge Level:

Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.

## Featured Solutions

Jamie counted stars and spots then drew a table to solve this
problem.

A variety of approaches were used to solve Squares in Rectangles.

Here is an easy proof of the Cauchy Schwarz inequality.

## Articles & Games

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

A Sudoku based on clues that give the differences between adjacent cells.