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This is a variation of a well known puzzle, you can find the other versions on PSE.

You have three ropes and a box with ten matches. As usual each rope takes one hour to burn completely when lighted from any end but it does not burn uniformly. This means (for example) that it could take five minutes to burn the first half and then 55 minutes to burn the remaining half. Or it could take 40 minutes for the first half and 20 for the second, you don't know. Each half does not burn uniformly too and the three ropes are different.

Every match lasts 5 seconds, so you have enough time to burn one or more ends of one or more ropes with the same match.

How do you measure exactly 1 hour and 8 minutes?

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    $\begingroup$ 1. Are you able to light things simultaneously? Like can I have things ignited the moment I want them ignited?* ”exactly 1 hour and 8 minutes”* makes me wonder about this. 2. Can matches be re-lit from the flame of the rope? 3. Can you light the exact middle of a rope? $\endgroup$
    – Cotton Headed Ninnymuggins
    Feb 12, 2020 at 3:59
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    $\begingroup$ (The above was posted by CHN as an answer because they didn't have enough rep to comment. Seems like a reasonable set of questions, so I've converted it to a comment.) $\endgroup$
    – Gareth McCaughan ♦
    Feb 12, 2020 at 13:39
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    $\begingroup$ 1. Yes, by joining multiple ends or ropes and lighting them with the same match; 2. no; 3. yes $\endgroup$
    – melfnt
    Feb 12, 2020 at 14:58

1 Answer 1

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Ok I will present a solution.

For convenience, I will number the ropes in the order of their burning.

STEP ONE

I will light up ROPE 1 from both the ends. At the same time, I will light another match and light up ROPE 2 from one end.ROPE 1 will take 30 min to burn off completely.(The average velocity of each flame remains the same). Till now, ROPE 1 is Burnt and two matches are gone. I have measured 30 minutes

STEP TWO

Now, as soon as ROPE 1 goes off, I will light up another match to light up the other end of ROPE 2. Simultaneously, I would use the same match to light up one end of ROPE 3. Thus, ROPE 2 will take 15 minutes(measured from Step One as zero reference). ROPE 1, ROPE 2 is Burnt and 3 matches are gone. I have measured 45 minutes.

STEP THREE

ROPE 3 is burning for 15 minutes. I will light another match to light the other end of ROPE 3. Thus, ROPE 3 will take 22.5 minutes to burn off completely (zero reference from Step Two). All ROPES are burnt and 4 matches are gone. I have measured 67.5 minutes.

FINAL STEP

I am left with 6 matches. Each one takes 5 seconds to burn. I will light them in such a order so that as soon as one goes off the other one starts burning. Thus they will take 0.5 minutes to burn.

Adding all the times. 30+15+22.5+0.5= 68 minutes.

I have successfully measured 1hour 8 minutes or 68 minutes

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    $\begingroup$ Well done. Did you find it difficult? $\endgroup$
    – melfnt
    Feb 8, 2020 at 18:31
  • $\begingroup$ Not much. But it was a GREAT PROBLEM. Definitely a teaser. rot13(Gur cneg erdhvevat gung gur nirentr irybpvgl bs synzr erznvaf fnzr naq gvzr trgf unyssrq bayl gbbx fbzr gvzr.) $\endgroup$
    – S K
    Feb 8, 2020 at 18:33
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    $\begingroup$ That's strange, because it's a standard way to solve this kind of puzzle (search this website for more). rot13 (V'ir nqqrq gur yngreny-guvaxvat gnt orpnhfr bs gur ynfg cneg va juvpu lbh unir gb ohea gur zngpurf, ohg nccneragyl vg vf gbb fvzcyr gb fbyir) $\endgroup$
    – melfnt
    Feb 8, 2020 at 18:43
  • $\begingroup$ @melfnt rot13(Bu Bxnl. V nterr jvgu lbh. V qba'g fpber zhpu ba zl VD grfgf. V thrff gung'f jul V sbhaq guvf ceboyrz 😅 dhvgr nirentr, abg fvzcyr.) $\endgroup$
    – S K
    Feb 8, 2020 at 18:47
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    $\begingroup$ Could you use only 1 match to light both ends of rope1, and one end of rope2? $\endgroup$
    – CSM
    Feb 9, 2020 at 14:59

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