Three Puzzles about a Math Toy
Recently, my wife bought the following wooden toy from a clearance bin at Target. It's a set of six dials, rainbow-colored, that are connected by a wooden axle. Photo Credit: eBay The dials are shaped like decagons, and each side of the dial is painted as follows: The red dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The orange dial: The following mathematical operators, in this order: +, -, x, +, -, x, +, -, x, +. Note that there are consecutive plus signs on the dial. The yellow dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The green dial: The = sign appears on all sides The blue dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 The purple dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Playing around with this toy, I came up with three puzzles. (Let me know if someone else has published these before!) Randomly (and independently) spin each of the six dials of the toy. Look at the mathematical statement that appears on the top of the toy. What is the probability that the mathematical statement is correct? Spin the dials so that ...