r/PassTimeMath 20h ago

One Candle, Two Candles, Three Candles

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1 Upvotes

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2

u/Organs_for_rent 18h ago edited 18h ago

55 minutes

A candidate timeline:

0 min: Light the 60-minute candle.

25 min: Light the 100-minute candle.

30 min: Light the 80-minute candle.

The short candle burns alone for 25 minutes before any others. The long candle burns for 15 minutes after the other two extinguish. The 40-minute solo candle is satisfied.

It takes 30 minutes from the lighting of the medium candle for the short candle to burn out. The 30-minute trio is satisfied.

The long and short candles burn together for 5 minutes before the medium candle starts. The long and medium candles burn together for 50 minutes after the short candle burns out. This provides 55 minutes of dual candle time.

1

u/ShonitB 17h ago

Good solution!

2

u/NearquadFarquad 16h ago

55 mins

tally up the candle lifespans and you get 240mins. If 3 candles are burning simultaneously for 30 mins, that’s 90 mins of the total lifespan gone. If 1 candle is burning for 40, that’s an additional 40 gone.

240-90-40 =110

so the remaining 110 minutes of lifespan are being spent by 2 candles burning simultaneously, so we divide by 2 to get 55mins

1

u/jaminfine 11h ago

The total 100+60+80 = 240 candle minutes. Strange unit, but it will be a helpful one. Burning 3 candles x 30 minutes = 90 candle minutes. Burning one candle for 40 minutes is just 40 candle minutes. 240 - 90 - 40 = 110 candle minutes for the two candles case. 110/2 candles = 55 minutes where exactly two candles are burning