While captured by the evil Dr Apocalypse, you are presented with a terrifying deathtrap. In front of you are five seemingly identical bottles full of pills, and a set of scales.
"Four of these bottles," explains Dr Apocalypse, "contain harmless sugar pills. Each of the harmless pills weighs 10 grams. One bottle, however, contains deadly poison that will deliver you to a painful death. Each of the poison pills weighs 9 grams."
"You may open the bottles, look at the pills, and use the scales I have provided you with once and once only. After you have made a single weighing of your choice, you must correctly identify the bottle of poison, or else be forced to eat a pill from it."
The scales are of the sort that return the total weight of everything placed on them (that is, pressure scales, not balancing scales). All the pills are shaped identically, and you're not allowed to weigh a pill and then keep adding more while still checking the weight. Only one weighing of as few or as many pills as you want, at once, is allowed.
How can you be certain which is the poison bottle? And what is the smallest number of pills you can weigh to arrive at that conclusion?
"Four of these bottles," explains Dr Apocalypse, "contain harmless sugar pills. Each of the harmless pills weighs 10 grams. One bottle, however, contains deadly poison that will deliver you to a painful death. Each of the poison pills weighs 9 grams."
"You may open the bottles, look at the pills, and use the scales I have provided you with once and once only. After you have made a single weighing of your choice, you must correctly identify the bottle of poison, or else be forced to eat a pill from it."
The scales are of the sort that return the total weight of everything placed on them (that is, pressure scales, not balancing scales). All the pills are shaped identically, and you're not allowed to weigh a pill and then keep adding more while still checking the weight. Only one weighing of as few or as many pills as you want, at once, is allowed.
How can you be certain which is the poison bottle? And what is the smallest number of pills you can weigh to arrive at that conclusion?
