Eureka!: Math Fun from Many Angles by David Lewis

By David Lewis

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If you are interested in investigating the strategy further, many manufactured versions are marketed; one model for the crafty is illustrated in Fig. 3-1. Fig. 3-1 DID YOU KNOW THAT ... 25 X 9 2 = 2592? 2. Another exciting variation of tic-tac-toe is played with moving counters, characteristically three to each player. Turns alternate for placing and, if neither player 37 has yet won, moving the counters commences. Usually, only moves along the orthogonals or perpendiculars are permitted, but variations which allow moves along the main diagonals (corner to corner) and/or the short diagonals are known.

If the cubie at uf should be at ur, perform (R 2D') 2 (F RL'U 2LR')(DR 2 ). 4. One hundred percent of the cubies are now correctly placed! Edge Orientation 1. Turn the entire cube so that one flipped edge is at ufo 2. Turn faces so that another flipped edge is at ub. 3. Perform either a or b: a. FUD'L2U2D2RU2R'D2U2L2DU'F'U2 b. (LR'F)(LR'D)(LR'B 2 )(RL'D)(RL'F)(RL'U 2) 4. Undo step 2. 5. Now go back to step 1. 6. Tell everyone within shouting distance: You've solved the cube!!! More Challenges Now go for speed, make pretty patterns, try odd colorings or cubes with unusually-shaped cubies, solve the new 4 X 4 X 4 cube, or try to solve the cube in the mirror.

3. Perform either a or b: a. FUD'L2U2D2RU2R'D2U2L2DU'F'U2 b. (LR'F)(LR'D)(LR'B 2 )(RL'D)(RL'F)(RL'U 2) 4. Undo step 2. 5. Now go back to step 1. 6. Tell everyone within shouting distance: You've solved the cube!!! More Challenges Now go for speed, make pretty patterns, try odd colorings or cubes with unusually-shaped cubies, solve the new 4 X 4 X 4 cube, or try to solve the cube in the mirror. Good luck! 68 EUREKA! ~oNiftY Numerics 6. Palindromesemordnilap _ _ _ _ _ __ A palindrome is a word or phrase that reads the same forward as backward, such as rotator or "Madam, I'm Adam" (to which she aptly replied, "Eve").

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