Question

The year is 1714. You are in a dark Spanish prison. You wake up to find yourself tied to a table with ropes. In the darkness you hear a rhythmic swishing sound-something going back and forth, back and forth. Eventually your eyes get accustomed to the dark and see that the source of the sound is a sharp bade at the end of a long pendulum that’s swinging back and forth over your body. With each sweep it gets a little lower-and a little closer to your chest. You note how long it takes between those swishes: exactly 7 seconds. And with each swish, the blade drops 1 inch lower. The last passing was only 15 inches above your chest. It won’t be much longer before the blade slices right through you. Should you scream for help? That would probably just summon a guard, who would run through with a sword then and there. But wait! You see a rat by your arms and he’s gnawing at the rope that binds you to the table. In fact, he has only 1 minute to go before he gnaws through it all the way. When he does that, you can get free! Will the rat chew through the rope before or after the blade has slashed through your chest? How much time do you have exactly?

Answer 1

If the rat will chew through the rope in 60 seconds you will be free.
In 7 seconds it will be 14 inches from your chest
In 14 seconds it will be 13 inches from your chest
In 21 seconds it will be 12 inches from your chest
In 28 seconds it will be 11 inches from your chest 
In 35 seconds it will be 10 inches from your chest
In 42 seconds it will be 9 inches
In 49 seconds it will be 8 inches
In 56 seconds it will be 7 inches
In 63 seconds it will be 6 inches  (and you will be free since the rat finished)
In 70 seconds it will be 5 inches
In 77 seconds it will be 4 inches
In 84 seconds it will be 3 inches
In 91 seconds it will be 2 inches
In 98 seconds it will be 1 inch
You have 6 seconds before it swings again and cuts you so you have 104 seconds exactly but lucky for you the rat chewed through the rope 44 seconds ago.