The Pit and the Pendulum
The Answer: The rat should chew through the rope 45 seconds before the pendulum blade reaches your chest.
1. You know that the rat will take 1 minute (60 seconds) to chew through the rope.
2. The pendulum blade is 15 inches above your chest and it lowers 1 inch with each swing. How many swings will it take the blade to reach you? Divide the height the blade is above you (15 inches) by the number of inches it drops per swing (1 inch). 15 swings
3. How long do 15 swings take, at 7 seconds per swing? Multiply the number of swings (15) by the number of seconds each swing should take (7). 105 seconds.
4. The rat should take only 60 seconds to chew through the rope, so the rat beats the pendulum.
5. To find out how much time you have to spare before the pendulum slashes through your chest, subtract the smaller amount of time (the rat’s 60 seconds) from the longer amount of time (the pendulum’s 105 seconds). 45 seconds. You have 45 seconds to spare before the blade hits you. Phew!!! Saved by the rat.
Winners: Andrew Gunyan, Maddy Johnson, Jamison Massey
The Cullinan Diamond Problem
On January 26, 1905 a 3,106-carat diamond was discovered in Pretoria, South Africa. Weighing nearly 1.5 pounds, the Cullinan, as it was named, is the largest diamond ever found. Since the greatest value in such a large diamond is in the number of stones that can be produced, renowned diamond cutter, Joseph Asscher, was chosen to cut the diamond. What remained after the stone was finally cut were nine major stones and 100 smaller stones totaling nearly 1,068 carats.
What percent of the diamond’s 3,106-carat total weight was lost as a result of cutting? Express your answer as a percent to the nearest tenth.