Two more puzzles

[Simon F]

Since the last puzzle thread proved popular, I thought I'd post a couple more that I saw on BBC 4's "Mind Games" show last night.

I suggest that if people want to post answers they use the

[size=4] answer text[/size]

formating so that it doesn't spoil it for others
test test test

Puzzle 1:
You have 5 bags of lollies/sweets/candies (depending on where you live). Four of them each contain 100 chocolate coated toffees which you adore. The other contains 100 chocolate coated peanuts to which you are allergic. All of the lollies look identical but you know that the toffees each weigh 1 gram while each peanut's weight is 1.1 grams. (The bags each weigh 10grams).

You have a set of very accurate kitchen scales (i.e. they tell you the weight (it's not a balance)) but you are only allowed to use them once. How do you identify the peanuts?


Puzzle 2:
You've got to bake a cake for 45minutes. Unfortunately all the clocks in the house have just broken but, luckily, you have two lengths of dynamite fuse (well, who hasn't?) that take exactly 1hr each to burn.

Unfortunately, the rate of burning is completely irregular - for example, it might take one fuse 59 minutes to burn 1/3rd of the way and then do the remainder in 1 minute.

How do you use them to time your cake?

 

[Joe DeFuria]

Clarification on question 1:

You have a set of very accurate kitchen scales (i.e. they tell you the weight (it's not a balance)) but you are only allowed to use them once. How do you identify the peanuts?

How many kitchen scales are in this "set?" And I'm a bit fuzzy on what may or may not constitute a "use".

 

[Simon F]

Clarification on question 1:

You have a set of very accurate kitchen scales (i.e. they tell you the weight (it's not a balance)) but you are only allowed to use them once. How do you identify the peanuts?

How many kitchen scales are in this "set?" And I'm a bit fuzzy on what may or may not constitute a "use".

Ahh the joys of English. How many? Exactly the same number as in a "pair of pants". One unit.

You may place "something" or "somethings" on the scales and read the result (at most) once.

 

[notAFanB]

regarding puzzle one, unless you worded it slightly incorrectly do *all* the bags weigh 10g, in which case you can't use the scales in any useful extent. am I misreading this?

if not then, pick one random bag and weigh it. if it weighs more than 10g then you are safe. if not you get to take away one bag safely?


regarding puzzle 2, can we cut/fold or in any way manipulate the fuses physically?

 

[Captain Chickenpants]

Ok, Puzzle 1
Have 1 sweetie from bag 1, 2 from bag 2 etc. Then see how many .1g the final weight has. e.g 15.3g would mean bag 3 is the heavier.



Not sure about puzzle 2!

CC

 

[MuFu]

Puzzle 1:
You have 5 bags of lollies/sweets/candies (depending on where you live). Four of them each contain 100 chocolate coated toffees which you adore. The other contains 100 chocolate coated peanuts to which you are allergic. All of the lollies look identical but you know that the toffees each weigh 1 gram while each peanut's weight is 1.1 grams. (The bags each weigh 10grams).

Can you take stuff out of the bags? I assume you can, otherwise you wouldn't have said they all look identical. Take a known quantity out of each bag then weigh the whole lot. You can tell which bag contains peanuts by the difference between the actual mass and what it should be assuming 1g per thingy.

MuFu.

 

[MuFu]

Oh crap, beaten to it by Chickenpants.

Will have to think about the 2nd one some other time too...

MuFu.

 

[Simon F]

regarding puzzle one, unless you worded it slightly incorrectly do

The cloth/plastic of each bag weighs 10grams, so a bag+100toffees would weight 110g.

Does that make it clearer?

 

[Simon F]

Ok, Puzzle 1

That is one possible possible solution - there are others that use the same principle.

Not sure about puzzle 2!

CC

It's a lot trickier to see the solution, IMHO, but it's really elegant.

 

[notAFanB]

regarding puzzle one, unless you worded it slightly incorrectly do

The cloth/plastic of each bag weighs 10grams, so a bag+100toffees would weight 110g.

Does that make it clearer?

yes thanks, in which case removing different quanties (non repeating) from each bag and weigh them . the total mass should have a discrepency which can be divided by only one of the sample from the bags.

 

[Simon F]

regarding puzzle 2, can we cut/fold or in any way manipulate the fuses physically?

You may... if you think it will help

 

[Captain Chickenpants]

Ok, don't think any of these are actually the correct answer but
A) Using a magnifying glass cut one of the fuses LENGTHWISE in half, and then half again. Giving you some strips which should burn for 45 seconds.
B) Using the scales from puzzle 1, weight the fuses and cut and reweigh them until you have managed to cut off 1/4 off the weight, stick the remaining bits back together again and you should have a fuse that burns for 45 mins


The key to the real answer presumably lies in the fact that you have two fuses. I guess that you need to use one fuse to light the second and can somehow use this to counteract the randomness of the fuse behaviour.




CC

 

[Joe DeFuria]

Puzzle 2

Assuming each fuse also gives off 0.605 Gigawats of power when completely burned.....light and place each fuse in a flux capacitor (we have dynamite fuses, why not a flux capacitor?) at the same time you put the cake in the oven. Then immediately set the time circuits for "15 minutes in the past". Upon completion of burning in one hour, the 1.21 gigawatts of power will activate the time machine and send you back 15 minutes. Take out the cake.

 

[Simon F]

Ok, don't think any of these are actually the correct answer but ...

Sorry no.

Since it is a bit tricky, I'll give a hint:
Life in the fast lane: You'd only need one fuse if your cake only needed 30minutes......

 

[Simon F]

Puzzle 2
....

Oh my! That was a lateral as a lizard on a sun lounge. I think the cake would be a bit smokey though.

 

[akira888]

Ok, don't think any of these are actually the correct answer but ...

Sorry no.

Since it is a bit tricky, I'll give a hint:
Life in the fast lane: You'd only need one fuse if your cake only needed 30minutes......

Puzzle 2:
Oh god, then it's trivial. Light both ends of the first fuse at the same time. It will burn out at 30 minutes. Light the first end of the second fuse at the same time. Then, at 30 minutes when the second fuse is half-burned light the second end of the second fuse. It will take 15 minutes for both ends to burn to the end of the second fuse, hence a total of 45 minutes.

 

[MuFu]

Hmm...

Is it something to do with lighting both ends of the fuse at the same time? 30 mins is up when the two flames meet.

[edit]Ok, got it. Late again though.

MuFu.

 

[Simon F]

Puzzle 2:
Oh god, then it's trivial. Light both ends of the first fuse at the same time. It will burn out at 30 minutes. Light the first end of the second fuse at the same time. Then, at 30 minutes when the second fuse is half-burned light the second end of the second fuse. It will take 15 minutes for both ends to burn to the end of the second fuse, hence a total of 45 minutes.

Congratulations. You have a perfectly baked cake.

 

[notAFanB]

assuming we don;t have an issue with matchsticks then maybe:


given an erratict of burning each fuse burns for exactly 1hr.

hence if both ends are lit then the fuse will burn out in 30 mins exactly. my reasoning for this i that if the rate of burn (god I hate that phrase) is irregular but predetermined then it would take the same time for the fuse to burn up in either direction.

by the same reasoning if we measure 30min tie span then we can reduce the 2nd fuse to it's remaining 30mins of length by simulataneously light one end.

subsequently lighting the other end of the 2nd fuse will again yield half the remaining time 15mins.

 

[Simon F]

Looks like a few have got it now. The answer is incredibly simple once you see it.