Well the only other solution that I can come up with is:
There are 4 possibilities of what we will see when we look at the coin - 3 of these will be heads and one will be tails. Since we see heads, we eliminate the fourth possibility so the probability of the other side being a head is 0.667.

F.

[edit] Rats!! Beaten to it[/edit]

That was my logic when i approached the problem.

Well Done to Zach! 1 Point... why don't you stick around, eh?

Standings:
1. Jason Gee - 5 Points
2. Fred - 3 Points
3. Gas Giant - 1 Point
4. JDWhale - 1 Point
5. Dominique - 1 Point
6. BeefDog - 1 Point
7. Zach Parker - 1 Point
8. TBD...

The Standings table looks a bit lackluster right now don't ya' think?! Five people on one point!

Fred, you were behind by about 1 minute, try again on the next question, eh!

Question 17: You are the foreman in charge of license plate production. Your equipment can produce two different gauges of steel, one weighing about 90% of the other. Normally you use the heavier gauge but one week you leave that responsibility to someone else who sets the gauge randomly every day. After a week you realize that some days the license plates may have been made of the lighter gauge steel. Every days license plates are kept in separate piles. You may use a digital scale once which will give an exact weight of whatever you decide to weigh. Assume that the heavy gauge license plates weigh 1 unit each and the light ones 0.9 units each. You may use the scale only once. How many license plates from each pile should you put on the scale?

Luke.

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- Luke.

Well Done to Zach! 1 Point... why don't you stick around, eh?

Standings:
1. Jason Gee - 5 Points
2. Fred - 3 Points
3. Gas Giant - 1 Point
4. JDWhale - 1 Point
5. Dominique - 1 Point
6. BeefDog - 1 Point
7. Zach Parker - 1 Point
8. TBD...

The Standings table looks a bit lackluster right now don't ya' think?! Five people on one point!

Fred, you were behind by about 1 minute, try again on the next question, eh!

Question 17: You are the foreman in charge of license plate production. Your equipment can produce two different gauges of steel, one weighing about 90% of the other. Normally you use the heavier gauge but one week you leave that responsibility to someone else who sets the gauge randomly every day. After a week you realize that some days the license plates may have been made of the lighter gauge steel. Every days license plates are kept in separate piles. You may use a digital scale once which will give an exact weight of whatever you decide to weigh. Assume that the heavy gauge license plates weigh 1 unit each and the light ones 0.9 units each. You may use the scale only once. How many license plates from each pile should you put on the scale?

Luke.

If I am reading this correctly it would be 9 heavy and 10 light to an identical weight.

Question 17: You are the foreman in charge of license plate production. Your equipment can produce two different gauges of steel, one weighing about 90% of the other. Normally you use the heavier gauge but one week you leave that responsibility to someone else who sets the gauge randomly every day. After a week you realize that some days the license plates may have been made of the lighter gauge steel. Every days license plates are kept in separate piles. You may use a digital scale once which will give an exact weight of whatever you decide to weigh. Assume that the heavy gauge license plates weigh 1 unit each and the light ones 0.9 units each. You may use the scale only once. How many license plates from each pile should you put on the scale?

Luke.

What are you trying to determine from the weighing?

F.

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Well Done to Zach! 1 Point... why don't you stick around, eh?

Standings:
1. Jason Gee - 5 Points
2. Fred - 3 Points
3. Gas Giant - 1 Point
4. JDWhale - 1 Point
5. Dominique - 1 Point
6. BeefDog - 1 Point
7. Zach Parker - 1 Point
8. TBD...

The Standings table looks a bit lackluster right now don't ya' think?! Five people on one point!

Fred, you were behind by about 1 minute, try again on the next question, eh!

Question 17: You are the foreman in charge of license plate production. Your equipment can produce two different gauges of steel, one weighing about 90% of the other. Normally you use the heavier gauge but one week you leave that responsibility to someone else who sets the gauge randomly every day. After a week you realize that some days the license plates may have been made of the lighter gauge steel. Every days license plates are kept in separate piles. You may use a digital scale once which will give an exact weight of whatever you decide to weigh. Assume that the heavy gauge license plates weigh 1 unit each and the light ones 0.9 units each. You may use the scale only once. How many license plates from each pile should you put on the scale?

Luke.

OK - going with some assumptions here:

Assuming that what we are trying to find is which days' production (if any) used the lighter gauge steel?

Use 1 from the day 1 pile
2 from the day 2 pile
4 from the day 3 pile
8 from the day 4 pile
16 from the day 5 pile

(and if it is a 7 day working week)
32 from the day 6 pile
64 from the day 7 pile.

F.

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I concur with Fred's answer: that's 2^(d-1) from each day, where d is the day number. That way the weight discrepency will easily show you which day (or days) the lighter steel was used. Doesn't pay to sleep around here .. Fred's Catching up :D

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"Living by the wisdom of computer science doesn't sound so bad after all. And unlike most advice, it's backed up by proofs." -- Algorithms to live by: The computer science of human decisions.

I concur with Fred's answer: that's 2^(d-1) from each day, where d is the day number. That way the weight discrepency will easily show you which day (or days) the lighter steel was used. Doesn't pay to sleep around here .. Fred's Catching up :D

Hi, Jason.

LOL. Maybe there should be an extra 1/2 point for defining the question as well? ;)

I have the advantage of being 1/2 day time shift away so keep your eye on the rear-view!!

F.

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Fred had the correct answer, Jason basically defined it. I see it as:
1 Point to Fred,
1/2 Point to Jason.

Congratulations both of you!

Standings:
1. Jason Gee - 5 1/2 Points
2. Fred - 4 Points
3. Gas Giant - 1 Point
4. JDWhale - 1 Point
5. Dominique - 1 Point
6. BeefDog - 1 Point
7. Zach Parker - 1 Point
8. TBD...

Question 18: You need to warm milk in a baby bottle from its initial temperature of 15 degrees centigrade to 25 degrees. You put the bottle in a pot of boiling water which stays at constant temperature of 100 degrees. The thickness and conductivity of the bottle are such that the initial rate of heat transfer is 85 degrees per minute. However heat transfer is proportional to the difference between the temperature of the milk and the water. How many minutes will it take to heat the bottle to 25 degrees?

Luke.

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- Luke.

If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

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http://www.therageclub.com

If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Hmmm not 100% sure. But I'll leave my first attempt!

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http://www.therageclub.com

Fred had the correct answer, Jason basically defined it. I see it as:
1 Point to Fred,
1/2 Point to Jason.

Congratulations both of you!

Standings:
1. Jason Gee - 5 1/2 Points
2. Fred - 4 Points
3. Gas Giant - 1 Point
4. JDWhale - 1 Point
5. Dominique - 1 Point
6. BeefDog - 1 Point
7. Zach Parker - 1 Point
8. TBD...

Question 18: You need to warm milk in a baby bottle from its initial temperature of 15 degrees centigrade to 25 degrees. You put the bottle in a pot of boiling water which stays at constant temperature of 100 degrees. The thickness and conductivity of the bottle are such that the initial rate of heat transfer is 85 degrees per minute. However heat transfer is proportional to the difference between the temperature of the milk and the water. How many minutes will it take to heat the bottle to 25 degrees?

Luke.

Q18: Reckon the rate of rate of change is -5 degrees per minute per minute and the time required to get to 25 degrees is 2 minutes.

F.

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If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Hmmm not 100% sure. But I'll leave my first attempt!

I can assure you that it takes longer than 7.5sec. to heat up a bottle by 10 degrees.

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If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Hmmm not 100% sure. But I'll leave my first attempt!

I can assure you that it takes longer than 7.5sec. to heat up a bottle by 10 degrees.

Ahh - the certainty born of (bitter?) experience ;)

Have to agree with you there D.

F.

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If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Hmmm not 100% sure. But I'll leave my first attempt!

I can assure you that it takes longer than 7.5sec. to heat up a bottle by 10 degrees.

Ahh - the certainty born of (bitter?) experience ;)

Have to agree with you there D.

F.

.1252 hours or about 7.5 minutes might be a better guess.

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If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Oppss I meant .1252 hours not minutes! Now I see my mistake (I think)!!!

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http://www.therageclub.com

If t=0 c=15, K=85
t=ln(85/(100-c))
if c=25 then
t=ln(85/(100-25))=ln(85/75)=0.1252 minutes...

Oppss I meant .1252 hours not minutes! Now I see my mistake (I think)!!!

Well, since you retract your original answer, I'll step in with it...
xfer rate of 85 degrees per minute... It would take much less than one minute to raise temp 10 degrees...

~ 0.1252 minutes

BeefDog, what is your final answer? .1252 minutes or .1252 hours?

Luke.

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- Luke.

BeefDog, what is your final answer? .1252 minutes or .1252 hours?

Luke.

Minutes is my final answer!

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http://www.therageclub.com

.1252 Minutes is the correct... Two people reached that answer...

So I see it like this:

1/2 Points to BeefDog
1/2 Points to JD...

It's only fair, since Beefdog retracted his minutes answer, before re-instating it.

Standings:
1. Jason Gee - 5 1/2 Points
2. Fred - 4 Points
3. JDWhale - 1 1/2 Points
4. BeefDog - 1 1/2 Points
5. Gas Giant - 1 Point
6. Dominique - 1 Point
7. Zach Parker - 1 Point
8. TBD...

Question 19 (1 Point):
Consider a infinite number of parallel lines, spaced one inch apart from each other. If you dropped a one inch toothpick at random on this set of lines what is the probability the toothpick would cross a line?

Luke.

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- Luke.

Would the possibility not be infinite as there are an infinite number of chances?

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