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        riddles >> easy >> Insomnia: Hours on Fire
        
(Message started by: alien2 on Apr 17^th, 2014, 8:35am)

Title: Insomnia: Hours on Fire
Post by alien2 on Apr 17^th, 2014, 8:35am

”They say time is the fire in which we burn.”

Dr. Tolian Soran

A man suffering from insomnia suddenly finds himself in a cubic room without openings of any kind. Although clueless about how he got there, his initial thoughts are that he fell asleep or is hallucinating. He observes the room. The room is moderately illuminated, as greenish glow-in-the-dark paint was applied to walls, ceiling and floor. The middle of the ceiling holds a cylindrical device that looks like a weapon. There are four candles on the floor in different sizes and each with a number. The numbers are 7, 9, 11 and 13 respectively. The last object on the floor as well as in the room is a matchbox holding matches.

A deep voice addresses him: "I am your mysterious captor. You were brought here for my amusement. I am not allowed to discuss my unique technology. I will just say that at all times I know everything what goes on inside the room.

The numbers on the candles tell exactly how many hours they burn. If you use the candles to measure 1 hr with no more than 5 min margin of error, I will cure you from insomnia and teleport you back home. If you fail to do that within 24 hrs given to you, I won't cure you. Instead, I'll activate the pain beam weapon and you'll experience severe pain for 60 s before I let you go."

Title: Re: Insomnia: Hours on Fire
Post by rloginunix on Apr 17^th, 2014, 9:36am

13 = A, 11 = B, 9 = C, 7 = D.

[hide]Light A, B, D.
Let them burn until A's height == C (9).
Extinguish B. B is now == 7, A == 9, D == 3.
Let A burn until it's height == B, 9 - 7 = 2 more hours of burning.
Extinguish A and D. A == 7, D == 1 hour left.[/hide]

Total cost == 6 hours.

Title: Re: Insomnia: Hours on Fire
Post by towr on Apr 17^th, 2014, 11:35am

I don't think you can assume [hide]their height is proportional to how long they burn. A, B and D might be long and thin, and C short and wide. Or some might be round and others cones[/hide]

[hide]Burn 13, 11 and 9 till 9 is burned up.
13 and 11 have now burned down to 4 and 2.
7-4-2=1, so light 7 and extinguish one of the others.
Wait till a candle is burned out and light the extinguished one again.
When it goes out, you have one hour of candle-light left.[/hide]

Title: Re: Insomnia: Hours on Fire
Post by rloginunix on Apr 17^th, 2014, 12:13pm

[hide]Light C and D.
When D burns out 2 hours left in C.
Light C from the other side == 1 hour of burning time.[/hide]

Title: Re: Insomnia: Hours on Fire
Post by towr on Apr 17^th, 2014, 1:02pm

I can't imagine that works in practice.
[hide]Even if you had a wick at the bottom, the wax would just drip on the floor, probably extinguishing the flame. Or if you keep it horizontal, then the wax drops from both end to the floor. In either case it'd burn/melt through the candle a lot quicker than twice as fast.
Granted, strictly speaking its stated the candles burn for exactly X hours, but then, strictly speaking, it wouldn't matter how many ends you light it from.[/hide]

Title: Re: Insomnia: Hours on Fire
Post by rloginunix on Apr 17^th, 2014, 2:18pm

I agree.

The fact that a novice like me made the assumptions that I made tells me (at least) that a slight problem statement disambiguation (if I may) may be beneficial:

"... using all four candles of varying densities (burning rates) and random shapes ..."

or

reword the problem in terms of hourglasses - [hide]you can put them on the side to stop the flow of sand[/hide]. Speaking of which, I think I have an hourglass problem.

Please look for "Snow White's Untigrumpynol" in this section.

[edit]
Snow White, not Cinderella.
[/edit