Math Riddles

Answer: 17 hours. At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half.

Answer: The back prisoner will yell "black" if there is an odd number of black hats in front of him and "white" if there is an even number of black hats in front of him. The next prisoner will then count the number of black hats in front of him and if it was odd and is now even, or vice versa, then that person knows what color their hat is. The next person then knows their hat color based on what the people before them said and how many black hats are in front of them. In this way the front 99 prisoners will know their hat color and will be set free. The prisoner in the back who goes first has a 50 percent chance of being set free.

Answer: Here are the two solutions. This is usually solved with guess and check although using logic may be faster. We know that each queen must be in it's own row vertically and horizontally. We also know that 4 of the queens must be on white and 4 on black. This is true because with 4 queens on the same color all of the rest of that color is venerable to attack. (It could be done with math).

Answer: Put three of the balls on each side. If they are even the ball that wasn't weighed is the light one. If they aren't even the side that is lighter has the light ball. Of these three balls, one should be put on each side. If the sides are even than the other ball is the light one. If they aren't even the one that is lighter is the ball you're looking for.

Answer: Trevor wins again. In the first race Trevor ran 100 meters in the time it took Tyler to run 95 meters. So in the second race when Tyler is at the 95 meter mark Trevor will also be there (since 100 - 5 = 95). Since Trevor is faster he will pass Tyler in the last 5 meters of the race.