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In this investigation you will look at the moves a Knight from a chess set might make on a 100 square. X The knight moves in an L shape. 2 left or right and 1 up or down X Or 1 left or right and 2 up or down From this starting position the knight could move to each of the squares marked with a circle. 1 11 21 31 41 51 61 71 2 12 22 32 42 52 62 72 3 13 23 33 43 53 63 73 The knight starts on 35, where 4 5could 6 it 7be after 8 9 one 10move? 14 15 16 17 18 19 20 24 25 26 27 28 29 30 34 35 36 37 38 39 40 44 45 46 47 48 49 50 54 55 56 57 58 59 60 64 65 66 67Draw 68 all 69 the 70 possible 74 75 76 77answers 78 79 on 80your 100 square. 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. 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 Route taken (squares landed on) Number of moves 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? 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? 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. 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. Your task is to plot a journey starting from 1 that visit every number up to 100. Is this possible? 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 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. 1= 1 11=1+22+14-26 2= 1+12+25-37 12= 1+22+3-5 3= 1+22+3-24 13= 1+13-1 4=1+22+3-22 14= 1+13 5= 1+22-3-15 15= 1+22+14-22 6= 1+13+25-33 16= 1+22+14-26+5 7= 1+13+5+17-29 17= 1+13+5+17+9-28 8= -1-13+5+17 18= -1+22 -3 9= 1+22-14 19= 1+13+15 10= -1-22 +33 20= 1+22-3 If you were able to complete this all your squares will be filled in. 1 11 21 31 41 51 61 71 2 12 22 32 42 52 62 72 3 13 23 33 43 53 63 73 4 14 24 34 44 54 64 74 5 15 25 35 45 55 65 75 6 16 26 36 46 56 66 76 7 17 27 37 47 57 67 77 8 18 28 38 48 58 68 78 9 19 29 39 49 59 69 79 10 20 30 40 50 60 70 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100