Burn the rope how to#
Burn the rope full#

Let's summarize the solution by collecting the steps together. This is how 45 minutes of time is measured. Both ropes burn out in $30 + 15 = 45$ minutes. Burning 30 minutes rest half-life of the second rope in double the burning speed of one end burning, takes 15 minutes.

This is same as burning the rest half-life of the second rope from both ends simultaneously. Result of last action: Other end of the second rope lighted up just as the first rope burns out in 30 minutes. Significance of burning the second rope from the other end just as the first rope burns out,

In 30 minutes more, rest of the second rope will be burned out.

The burning point is still alive in the second rope and is moving towards its opposite end.

30 minutes burn time of second rope still left.

Burn the rope full#

Half the full burn time of 1 hour of the second rope is spent. 30 minutes half-life of the second rope and NOT ITS HALF LENGTH burns out.What happens when the second rope starts to burn first time from one end simultaneous to burning first rope from both ends? To be sure, let us examine burning the second rope in more details. This is an intriguing riddle where the solution is reached by finding the ONLY FEASIBLE course of action, though we do not know yet how 45 minutes will elapse after the actions are taken. Though reason says, there cannot be any other way 45 minutes can be measured, we are not satisfied. When should we light up the second rope at its other end?įact: The only known point of time to burn the other end is when the first rope burns out.Ĭonclusion 8: This is when we must start to burn the other end of the second rope. So continue to reason based on knowledge gained till now.Ĭonclusion 7: As a rope cannot be burned only from one end, the second rope must be burned from its other end as well. This is the second breakthrough achieved by step by step reasoning.īut solution not yet reached. No way 45 minutes target can then be met.Ĭonclusion 6 on action Step 2: Burn the second rope only at one end simultaneous to burning the first rope at both ends. So,Ĭonclusion 4: The second rope must burn only from one end.Ĭonclusion 5: Burning of the second rope cannot start AFTER the first rope burns out. In both infeasible actions, the second rope burns from both ends. If the second rope burns from both ends just as the first rope starts to burn from both ends, both ropes will burn out in 30 minutes.If the second rope burns from both ends just AFTER the first rope burns out, it'll take 30 minutes more to burn out.

Burn the rope how to#

A time less than 45 minutes is measured in the first step of burning one rope.Ĭhallenge is now, how to burn the unused second rope to measure 15 minutes more. The rope will burn in 30 minutes, not in 1 hour. So, no rope can be burned from only one end.įrom the two conclusions, decide the first action,Ĭonclusion 3 on action Step 1: Burn one rope from both ends simultaneously. On further analysis, make the second key conclusion,Ĭonclusion 2: As burning a rope from only one end will burn it in one hour, target time of 45 minutes will be exceeded. Solution to the two burning ropes timer riddle: Step by step reasoningįrom the information, draw the first key conclusion on what cannot be done,Ĭonclusion 1: As the ropes burn at non-uniform rates along the length, each rope can be burned only from the ends. Only saving grace is the allowance that one or both of the ropes can be burned simultaneously at multiple points. That's why you cannot just measure a point at three-fourth of the length of a rope and start burning at that point to measure 45 minutes. The ropes are of same length but none of the two burns at a uniform rate throughout the length. Measure a time of 45 minutes by burning two ropes each of which takes 1 hour to burn out.