1. In this investigation you will look at the moves a Knight from a chess set might make on a 100 square.

2. X X The knight moves in an L shape. 2 left or right and 1 up or down Or 1 left or right and 2 up or down

3. From this starting position the knight could move to each of the squares marked with a circle.

4. 80797877767574737271 70696867666564636261 60595857565554535251 50494847464544434241 40393837363534333231 30292827262524232221 20191817161514131211 10987654321 The knight starts on 35, where could it be after one move? Draw all the possible answers on your 100 square.

5. The Century Knight wants to get to the 100 square. Your task is to plot the journey from 1 to 100 in the fewest number of moves.

6. 1) Break the problem into smaller pieces 2) Tabulate results 3) Look for patterns and why they occur 4) Find a formula 5) Solve the problem

7. Route taken (squares landed on) Number of moves

8. The Century Knight wants to get to the 100 square. Your task is to plot the journey from 1 to 100 in the fewest number of moves. The minimum number of moves is 6 One such route is 13, 25, 37, 58, 79,100 Do you have another?

9. The Square Knight has to see all the square numbers. Plot a journey that visits every square number. Is this possible? What is the shortest path?

10. The Cube Knight has only the cube numbers to inspect. Plot a journey that visits all the cube numbers up to 100, starting from 1. Is this possible? What is the shortest path? What is the shortest path if you visit them in ascending order.

11. The Target Knight combines the numbers from each square it visits using addition or subtraction. For example: 1+22-14= 9 1+13-1 = 12 Your task is to find ways of making all the numbers 1 to 20.

12. Your task is to plot a journey starting from 1 that visit every number up to 100. Is this possible?

13. The Square Knight has to see all the square numbers. One possible journey is 1, 13, 25, 4, 16, 28, 9, 30, 49, 57, 36, 44, 56, 64, 83, 62, 81, 73, 85, 77,98, 79, 100

14. The Cube Knight has only the cube numbers to inspect. Plot a journey that visits all the cube numbers up to 100, starting from 1. A 10 move journey: 1,13, 25, 6, 27, 8, 16, 24, 45, 64 Or in ascending order: 1,13, 5, 17, 29, 8, 27, 35, 56, 64 This is also 10 moves.

15. 1= 1 2= 1+12+25-37 3= 1+22+3-24 4=1+22+3-22 5= 1+22-3-15 6= 1+13+25-33 7= 1+13+5+17-29 8= -1-13+5+17 9= 1+22-14 10= -1-22 +33 11=1+22+14-26 12= 1+22+3-5 13= 1+13-1 14= 1+13 15= 1+22+14-22 16= 1+22+14-26+5 17= 1+13+5+17+9-28 18= -1+22 -3 19= 1+13+15 20= 1+22-3

16. If you were able to complete this all your squares will be filled in.

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