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# Poly Plug Puzzles B

 These notes begin with support for turning each menu item into a whole class investigation, then link to the companion Task Cameo, which in turn links to Maths300 (where appropriate). These investigations involve Logic & Reasoning and are suitable for Year Levels: 3 - 8 Discover Menu Maths here. Order Poly Plug here.

### Back To Back Building

This task is a 3d activity using cubes that connect in three dimensions. One student secretly makes a shape, the students sit back to back, and the second student has to rebuild the shape from the first student's instructions only. This can't be exactly reproduced with Poly Plug, but the same principle is involved in the activity Copy Cats stored in Calculating Changes. Also in Calculating Changes you will find that children from West Ulverstone Primary School invented the same activity for themselves and called it Poly Plug Pictures.

Task 60, Back To Back Building

### Crossing The Desert

#### Equipment

• One Poly Plug set per pair

#### Problem

Two travellers set out on a 9 day journey across a desert to deliver a message and return with the answer. They can each only carry enough food for 12 days. How can the message be delivered and the answer returned?

#### Procedure

See the Task Cameo for a full explanation and a printable playing board. One red board supplies the 24 pieces of food that can be carried by the two travellers and they can then be made into piles moved across the desert by two students acting as the travellers. The students will soon realise that one must be the messenger and one is along to carry (and bury food). But on which days and how many portions?
• How many solutions are there?
• How do you know when you have found them all?

### Nim

#### Equipment

• One Poly Plug board per pair - it doesn't matter which colour

#### Problem

This task is a game with these rules.
• Arrange plugs like this to begin the game.
• Players take turns to remove one or more plugs from one row. This includes being allowed to remove the whole row.
• The loser is the person who takes the last plug.
The problem is to find a winning strategies.

#### Procedure

1. Introduce the game and invite students to play it a few times.
2. Discuss anything students have noticed about the game and suggest that you want their assistance to find a way to be sure of winning.
Have there been any times when you knew you were going to win? How did you know?
3. Encourage further investigation with a focus on knowing when you are going to win (or lose).
4. It should start to become clear that you can win if you leave your opponent with an odd number of moves to the end, for example:
The investigation now becomes a search for other positions to leave your opponent which will cause them to lose.
5. Make a classroom display of the winning strategies that students discover over time.

### Human Moves Monster

#### Equipment

• One Poly Plug set per pair or per person

#### Problem

Nine monsters are placed in a given arrangement on a 5x5 grid. These are the blue plugs in the red board. The human is shown with a yellow plug. The human begins in any unoccupied gap and moves as a knight in chess, that is, one cell left/right or up/down combined with one move diagonally to the next gap after that. The diagonal move cannot make a 'sharp' angle. The human can jump over monsters as part of the move and it captures a monster when the end of any move is on a monster. The aim is to capture all the monsters in the least number of moves.