Mount Mercy Maths Circle: Week 2

02/02/2012

Sophie Scannell and Sophie Daly

Lesson Plan

  1. Discussion of homework problems;
  1. Lazy gardener and diligent gardener problem
  2. Fox, chickens and oats problem
  3. Two boys and a boat problem

(All contained in lesson plan one)

  1. Matchstick problems;
  1. Cherry in the glass
  2. Turning the fish
  3. Two squares to three squares
  4. Three triangles to four triangles

(See end of document for diagrams)

  1. Physical problems;
  1. Water in jugs problem
  1. Magic circles

We start with the diagram below.

The objective is to place the numbers 1,2,3,4,5 and 6 in the smaller circles below so that the numbers along the circumference of each big circle adds up to 14.

  1. Three lightbulbs problem

“There are three light bulbs in a room, and three light switches outside the room. You are outside, and want to match up which switch goes with which light bulb. You can only travel into the room once, and cannot come back in again. You can do anything you want upon entering the room. How can you set the situation so that you will know which switch corresponds with which light bulb?”

  1. Number problems;
  1. Gauss’ method for adding 1 – 100
  1. Countdown (as last week)
  1. Homework;
  1. Seven Bridges of Konigsberg

The city of Königsberg (now Kaliningrad) used to have seven bridges across the river, linking the banks with two islands. The people living in Königsberg had a game where they would try to walk across each bridge once and only once. You can choose where to start.

  1. Traffic jam game

There are seven stepping-stones and six people. On the three left-hand stones, facing the center, stand three of the people. The other three people stand on the three right-hand stones, also facing the center. The center stone is not occupied.

The challenge: exchanging places

Everyone must move so that the people originally standing on the right-hand stepping-stones are on the left-hand stones, and those originally standing on the left-hand stepping-stones are on the right-hand stones, with the center stone again unoccupied.

The rules:

  1. After each move, each person must be standing on a stepping stone.
  2. If you start on the left, you may only move to the right. If you start on the right, you may only move to the left.
  3. You may "jump" another person if there is an empty stone on the other side. You may not "jump" more than one person.
  4. Only one person can move at a time.

Diagrams for Matchstick puzzles;