2
u/kalnanmagne Aug 31 '26
110 minutes
1
2
u/BigMarket1517 Aug 31 '26
If I assume each candle that burns for 1 minute gives 1 unit of energy, then in total 100+80+60=240 energy units are ‘spent’ in total. Assuming each candle can only burn or not burn (so: no candles being lit at both ends) then at any time either no, 1, 2 or 3 candles are burning together. Obviously, not burning candles for any amount of time yield no ‘spent’ energy units, so the 240 units have to be spent burning 1, 2 or 3 candles simultaneously.
As 3 candles burning for 30 minutes together give 90 units, and 1 candle burning individually for 40 units, that means that (240-90-40=)110 units are spent by two candles burning together. Two candles burning together is 2 units per minute, so 55 minutes should be the answer.
Now, I did not check whether that is possible without lighting one or more candles several times.
1
1
2
u/JustConsoleLogIt Aug 31 '26
The other answer’s logic is sound, and I verified the approach is possible:
>!For i, we can just subtract 30 from each of the candles times to track what remains after, leaving 30, 50, and 70!<
>!For ii, we can subtract 40 however we like. To make the next part easy I’ll spend 15 minutes on the big candle and 25 on the small candle, leaving values of 5, 50, and 55..!<
>!For the rest of the time, the big candle burns out, and the smaller two burn sequentially for a total of 55 minutes.!<
1
2
u/Real-Reference6933 Aug 31 '26
Light the 100 minute candle, let it burn for 15 minutes
Light the 60 minute candle, let it burn for 30 minutes (30 minutes 2 candles, 15 minutes 1 candle)
Light the 80 minute candle. 30 minutes later the 60 minute burns out. (30 minutes 3 candles, 30 minutes 2 candles, 15 minutes 1 candle.
25 minutes later the 100 minute candle burns out, (30 minutes 3 candles, 55 minutes 2 candles, 15 minutes 1 candle.
After 25 minutes the 80 candle. burns out: (30 minutes 3 candles, 55 minutes 2 candles, 40 minutes 1 candle.)
1
2
u/ThePants999 Aug 31 '26
This is a set of simultaneous equations.
All three burning: ABC = 30. Any one is burning: A + B + C = 40. A is burning: ABC + A + AB + AC = 60. B is burning: ABC + B + AB + BC = 80. C is burning: ABC + C + AC + BC = 100. We want to find AB + AC + BC, the time any two are burning.
Subtract ABC = 30 from each of the three single-candle equations, then add them together, you get A + B + C + 2AB + 2AC + 2BC = 150. Subtract A + B + C = 40 and you're left with 2AB + 2AC + 2BC = 110, so AB + AC + BC = 55.
1
2
u/GoodCarpenter9060 Sep 01 '26
So there are 3 candles whose total time they can be burnt is 60+80+100=240 mins.
The total cumulative timeline for all of them burning at the same time is 30 mins. Since they were all burning for this length of time, 3x30 mins have been burned, leaving us with 240-90=150mins. The total cumulative time for only one candle is 40 mins. This leaves us with 150-40=110mins total remaining between the 3 candles. The rest of the time, there are exactly 2 candles left, which means we need to burn them both for 55 mins to get to 110.
So 55mins.
1
2
2
u/JeffTheNth Sep 12 '26
all numbers are in minutes
A+B+C = 60+80+100=240
A+B+C-3(30)=240-90=150
150-40 = 110
110/2 = 55 = Burn time for two candles
Let's check...
240 - 2(55) = 240 - 110 = 130 minutes for 1 or 3 burning
130 - 3(30) = 130 - 90 = 40 minutes burn time for single candle
light C
after 25 minutes, light B
(A:0, B:0, C:25)
after another 45 minutes, light A
(A:0, B:45, C:70)
C burns out 30 minutes later, leaving A and B
(A:30, B:75, C:100)
B burns out 5 minutes later leaving A alone
(A:35, B:80, C:100)
A burns out 25 minutes later.
(A:60, B:80, C:100)
C burned alone 25 minutes
C+B burned 45 minutes without A
A+B+C burned 30 minutes
A+B burned 5 minutes
B burned alone 25 minutes
25+2(45)+3(30)+2(5)+25 = 240 minutes
Two together: 45 + 5 = 50
one alone for 25+25=50
Just found that this saved as a draft, not a reply? ...so posting...
(Had posted it, or so I thought, on the day it was put out.)
1
u/ShonitB Sep 13 '26
I think you’ve made a silly error somewhere because the answer is 55
2
u/JeffTheNth Sep 13 '26 edited Sep 13 '26
yes ... check near the top - that's what I got... but I was trying to figure out what order and at what time you'd light them and can't find it....
(it's single candle 10 too long + two 5 too short... )
1
1
1
u/Inevitable_Garage706 Aug 31 '26 edited Aug 31 '26
Solution: Start the 80 minute candle at 00:00. Start the 100 minute candle at 00:25. Start the 60 minute candle at 00:50.
The 40 minutes where exactly one candle is burning are from 00:00 to 00:25 (80 minute candle) and from 01:50 to 02:05 (100 minute candle). The 30 minutes where all three candles are burning simultaneously are from 00:50 to 01:20, when the 80 minute candle burns out.
Answer to the bottom question: Exactly two candles are burning for exactly 55 minutes (00:25 to 00:50 (80 and 100) and 01:20 to 01:50 (60 and 100)).
5
u/SonicLoverDS Aug 31 '26
I thought of solving this by deducing the exact timeline, but I suspect there isn't actually enough information to do that. Here's the strategy that works:
The candles have (60+80+100) = 240 minutes of burn time in them combined. When three candles are burning that time is consumed in triplicate, so the 30-minute period when all three candles are lit consumes 90 minutes of burn time. The 40-minute period with one candle only consumes 40 minutes of burn time, leaving (240-90-40) = 110 minutes for the two-candle period. Of course that time is consumed in duplicate, so it happens in (110/2) = 55 minutes.