Poll

8 votes (47.05%)
6 votes (35.29%)
3 votes (17.64%)
2 votes (11.76%)
6 votes (35.29%)
2 votes (11.76%)
3 votes (17.64%)
2 votes (11.76%)
8 votes (47.05%)
6 votes (35.29%)

17 members have voted

rsactuary
rsactuary
Joined: Sep 6, 2014
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Thanks for this post from:
CrystalMath
July 30th, 2020 at 4:30:46 PM permalink
Hint: it's not by spamming 10 different threads with the same question.
Gialmere
Gialmere
Joined: Nov 26, 2018
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July 30th, 2020 at 4:40:57 PM permalink
Quote: charliepatrick

Let's assume the candles were originally 12" tall. So the large one (L) burns at 3" per hour, and the small one (S) at 4" per hour.

After 2 hours L has lost 6" so has 6" left; S has lost 8" so has 4" left. After 3 hours L has lost 9" so has 3" left, S has now just burnt out.

So let t be the time before 3 hours. The height of the large one is L=3+3t, the height of the small one is S=4t.
At the time of the solution L=2S.
So 8t=3+3t; 5t=3, t=3/5.

So after 2 2/5 hour...
...the large candle is 12-(2.4*3) = 12-7.2 = 4.8" tall
...the small candle is 12-(2.4*4) = 12-9.6 = 2.4" tall.

So the time is 2 hours 24 minutes.


Quote: Wizard


I see I agree with Charlie, but I want to get credit anyway...

Let:
a = Time remaining on thick candle
b = Time remaining on thin candle
t = Time candle burned.

a = 4-t
b = 3-t

The height of each candle will be proportional to it's remaining time to it's beginning time.

Ratio of height left of a = (4-t)/4
Ratio of height left of b = (3-t)/3

Let's say each candle starts at 12". At some time x, the thick one will be twice as tall. In other words,

12*((4-t)/4) = 2*12*((3-t)/3)
3 * (4-t) = 8 * (3-t)
12 - 3t = 24 - 8t
5t = 12
t = 2.4

So, the candles have burned for 2.4 hours.

Good puzzle.


Correct!
----------------------------

My wife said if I bought her one more stupid gift she would burn it.

So I bought her a candle.
Have you tried 22 tonight? I said 22.
Wizard
Administrator
Wizard
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July 30th, 2020 at 5:26:31 PM permalink
Speaking of candles.

You have a box of matches and six 64-minute candles. Candles may burn from either or both ends. Each candle burns exactly 64 minutes but the rate of burning is inconsistent. A half a candle would not necessarily burn in 32 minutes. The candles are also not equally inconsistent. Two cut candles of the same length would not necessarily burn in the same time. Without the use of a clock, scissors, or anything other than the matches and the candles how can you create a 60-minute candle?
It's not whether you win or lose; it's whether or not you had a good bet.
Ace2
Ace2
Joined: Oct 2, 2017
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July 30th, 2020 at 5:50:41 PM permalink
Deleted
Itís all about making that GTA
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
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July 30th, 2020 at 5:52:23 PM permalink

Do you need 6? I can do it with 5

Label five of the candles A, B, C, D, and E
Light both ends of candle A, and one end of candles B, C, and D
32 minutes later, candle A is extinguished, and B, C, and D have 32 minutes left; light the other end of candle B
16 minutes later, candle B is extinguished, and C and D have 16 minutes left; light the other end of candle C
8 minutes later, candle C is extinguished, and D has 8 minutes left; light the other end of candle D, and one end of candle E
4 minutes later, candle D is extinguished; extinguish candle E, which is now a 60-minute candle

Wizard
Administrator
Wizard
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July 31st, 2020 at 1:58:18 AM permalink
Don, you seem to be right, you do need only five. Well done.
It's not whether you win or lose; it's whether or not you had a good bet.
Ace2
Ace2
Joined: Oct 2, 2017
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August 1st, 2020 at 8:26:29 PM permalink
Starting with a new shooterís first roll, what the expected number of rolls to resolve the fire bet (all six points)?
Itís all about making that GTA
Wizard
Administrator
Wizard
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August 1st, 2020 at 8:56:30 PM permalink
Quote: Ace2

Starting with a new shooterís first roll, what the expected number of rolls to resolve the fire bet (all six points)?



Do you mean to win the Fire Bet?
It's not whether you win or lose; it's whether or not you had a good bet.
Ace2
Ace2
Joined: Oct 2, 2017
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August 1st, 2020 at 10:17:35 PM permalink
Quote: Wizard

Do you mean to win the Fire Bet?

To resolve it. To win or lose it. Must be all six points to win

A recent thread basically asked whatís the lowest edge (per roll) wager on the table. Though technically the fire bet probably doesnít qualify, it got me thinking what the edge per roll might be.
Itís all about making that GTA
avianrandy
avianrandy
Joined: Mar 7, 2010
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August 2nd, 2020 at 1:57:08 AM permalink
On your rotating dice image, I am never seeing the number 3. Am I missing something lol?

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