Today we started “Grasshopper Games” in class. You found that for one piece, the number of moves would always be equal to one less than the sidelength of the board. (m=s-1). For four pieces, you found that adding to the sidelength would always add two more moves. (m=2s-3)

Use your board to determine the fewest moves (m) it takes to move nine pieces from one corner of the board to the other on any sized (s) board greater than 6. You should have a formula written for next week and be able to explain why it works.

Solve the second “HEX-7” problem.  Your solution should be foolproof.  Write up your solution in a way that describes, step by step, how your moves will lead to a win.  I encourage you to use diagrams and to label your board (A-D and 1-4) so that your explanations are clear.

 Due after winter break:Play hex-7 at least three times with a parent.  Then read about the game’s strategy on mazeworks.  At the end of the pages about hex strategy, there are three problems.  In each one, white makes the next move that will force a win.  Solve two of these puzzles for homework.  Bring your solutions to class.

Tower of Hanoi

Use this applet to find the number of moves (M) it would take for any number of discs (D).

Write one page describing your strategy and how it connects to the formula.  Use diagrams if you need them.  Your writing should be proofread and all diagrams must be made neatly.

Do patterns D, E and F for homework.  For each pattern, copy the first three stages, draw the 4th and 5th, and write about what you notice.  Thn create a table for stages 1-10 and write a formula to describe the number of dots at any stage.  Prove it works by calculating the number of dots at the 100th stage.