developing mathematical reasoning with games and puzzles · developing mathematical reasoning with...
TRANSCRIPT
© 2012 Michael Serra
Developing Mathematical Reasoning with Games and
Puzzles
HCTM Maui Hawaii September 22, 2012 with Michael Serra
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© 2012 Michael Serra 2
Rook's Tour Puzzles Starting anywhere, add the missing numbers from 1 through 81 so they follow a horizontal or vertical path (no diagonals). The empty circles in the Rook's Tour Puzzle on the right are the first (1) and last (81) numbers in the tour.
King's Tour Puzzles
King’s Tour Puzzles: Starting anywhere, fill in the missing numbers from 1 through 25 in the puzzle on the left so that a chess king can create a path from the 1 to 2 to 3 and so on to the 25. Fill in the missing numbers from 1 through 36 in the puzzle on the right so that a chess king can create a path from the 1 to 2 to 3 and so on to the 36. The squares with the white circles are the starting and ending squares in the king’s path.
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47 46 43 42 33 32 31 24 23
69 70 71 72 73 74 3 2 1
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7173 67
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37 4741 45
19 23
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© 2012 Michael Serra 3
Knight's Tour Puzzles
Starting anywhere, fill in the missing numbers from 1 through 25 in the Knight's Tour puzzle on the left so that a chess knight can move from the 1 to the 2 to 3 and so on all the way to the 25 without ever landing on the same square twice. Fill in the numbers from 1-64 in the puzzle on the right. The squares with the white circles are the starting and ending squares in the knight’s path.
Magic Square Puzzles
A magic square puzzle is an incomplete magic square. In a magic square, the sum of the numbers in each row, column, and both main diagonals have the same sum, called the magic sum.
If the n2 numbers in an nxn magic square are the positive integers 1 through n2, then the magic square is normal. If not then it is a simple magic square. The magic square puzzle to the left is a normal 5x5 magic square and the magic square puzzle to the right is a normal 6x6 magic square. Complete the magic squares.
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6 35 1
7 11 28
14 16 24
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25 29 9
5 33 4 2 31
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© 2012 Michael Serra 4
Knight's Tour Semi-Magic Square Puzzles
If the sums in the two main diagonals in a magic square do not add to the magic sum then it is a semi-magic square. In a knight’s tour semi-magic square it is possible to move the chess knight from the 1 to 2 to 3 and so on all the way the last number in the magic square. If it is on an 8x8 grid (chess board) then each row and column have the same sum and the knight can move from 1 to 2 to 3 and so on up to 64. Complete the 8x8 semi-magic knight’s tour.
1 48 18
30 46 62 14
2 32 34 64
29 45 20 61 36
5 25 9 40 60
28 53 41 24 12 37
43 55 10
42 7 58 23
© 2012 Michael Serra 5
Racetrack 1. A car can maintain its speed in either direction or it can change speed by only one
unit distance per move either horizontally, vertically, or both. Since you are not moving at the start, your pre-game speed is (0,0).
2. The new grid point and the segment connecting it to the preceding grid point must lie entirely within the track.
3. No two cars may occupy the same grid point at the same time (no crashes).
© 2012 Michael Serra 6
© 2012 Michael Serra 7
Buried Treasure
Your Treasure Positions Opponents Treasure Positions
Your Treasure Positions Opponents Treasure Positions
© 2012 Michael Serra 8
Your Treasure Positions Opponents Treasure Positions
Your Treasure Positions Opponents Treasure Positions
90°
270°
180° 0°
45°135°
225° 315°
90°
270°
180° 0°
45°135°
225° 315°
© 2012 Michael Serra 9
Resources • Smart Moves Developing Mathematical Thinking with Games and Puzzles, Serra, Playing It Smart
• Discovering Geometry 4th edition, Serra, Kendall Hunt Publishing • The Canterbury Puzzles, H.E. Dudeney, Dover • Mathematical Diversions from Scientific American, Martin Gardner, Simon & Schuster
• Mathematical Recreations and Essays, W.W.R. Ball & H.S.M. Coxeter, Dover • How To Solve Sudoku, Robin Wilson, The Infinite Ideas Company • The Zen of Magic Squares, Circles, and Stars, C. A. Pickover, Princeton University Press
• Professor Stewart's Cabinet of Mathematical Curiosities, Ian Stewart, Basic Books • Polyominoes, Solomon Golomb,Charles Scribner’s Sons
Website • www.michaelserra.net
Email •personal: [email protected] •professional: [email protected]