# The Naked Scientists Forum

### Author Topic: Try solving these easy problems by deductive thinking  (Read 45096 times)

#### lightarrow

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« Reply #100 on: 20/11/2008 07:53:01 »
A sample of 100 kg of potatoes has a water content of 99%. It is put under the sun to dry a little, and the water content at the end becomes 98%. How does the potatoes weight now?
Is the water content 97.02%? Do the potatoes weigh 98kgs?
No, the water content, at the end, is exactly 98% and the potatoes weight is not 98 kg.

#### RD

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« Reply #101 on: 20/11/2008 16:59:00 »
you have two fuses which burn exactly in one hour each; they don't burn in a regular way, however, so you can't say that half  lenght will burn in half an hour, and so on.
The problem is that you have to measure exactly 45 minutes. How will you do it?

My solution requires two conditions:-
a) that both fuses, although  they do not burn at a constant rate, are identical: their varying burn rate is the same in both fuses.
b) it is possible to discriminate the ends of the fuses, so they can both be lit from the same end.

Solution:-
1) place one fuse in a loop, to form the letter “O”, so both ends of the fuse can be lit simultaneously.
When the two  flames meet in the “O” half an hour will have elapsed. Mark the point on the fuse at which the two flames meet,
(this point is probably not the midpoint as the fuse did not burn at a uniform rate).

2) Transfer this mark to the same position on the second fuse. Make this fuse into a letter “P” with the loop of the “P” starting at this mark. Light the base of the “P”, when the single flame reaches the loop of the “P”  half an hour will have elapsed, the loop of the “P” will then burn with two flames like the “O”, the loop of the “P“ will burn in 15 minutes.  So the “P” fuse will take 45 minutes to burn out.
« Last Edit: 20/11/2008 17:01:44 by RD »

#### lightarrow

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« Reply #102 on: 20/11/2008 20:16:07 »
It's possible to solve it without your assumption a) but with b) only.

#### Alan McDougall

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« Reply #103 on: 22/11/2008 08:48:16 »
Hello,

Here are a few more problems to solve, the first few easy and the last a little more difficult. If interest is shown I will come in with other perplexing puzzles or problems of logic some more difficult and the others much easier to keep the topic as fun thread

1) The Frog
A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

2) The Socks
Cathy has six pairs of black socks and six pairs of white socks in her drawer.
In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?

3) There is something about Mary
Mary's mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?

4) 100 Gold Coins (this problem is more difficult)

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

« Last Edit: 22/11/2008 08:50:41 by Alan McDougall »

#### lightarrow

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« Reply #104 on: 22/11/2008 18:09:38 »
It's possible to solve it without your assumption a) but with b) only.

Ok, I'll give the solution, it seems a very difficult problem!

1.Light simultaneously the two ends of the first fuse and one end of the second.
2.After exactly 30 minutes the first fuse will be completely burnt and the second will have exactly other 30 minutes to burn.
3.At this moment, light the second end of the second fuse.
4.After exactly 15 minutes from that moment, the second fuse will be completely burnt. 30 + 15 = 45 minutes.

I have to admit that, even if the solution is quite simple, I wasn't able to find it.
« Last Edit: 22/11/2008 18:11:44 by lightarrow »

#### lightarrow

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« Reply #105 on: 22/11/2008 18:14:42 »
1) The Frog
A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

29 days, I suppose!

Quote
2) The Socks
Cathy has six pairs of black socks and six pairs of white socks in her drawer.
In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?

3 socks, I suppose!

Quote
3) There is something about Mary
Mary's mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?

Mary, I suppose!

Quote

4) 100 Gold Coins (this problem is more difficult)

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?
No idea how to solve it...

#### erickejah

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« Reply #106 on: 23/11/2008 02:44:40 »
Me too - I can solve it in two weighings if I cheat and use either gravitational attraction or momentum, but not purely via weighing.

can u be more explicit with those methods please.

#### SquarishTriangle

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« Reply #107 on: 23/11/2008 04:44:28 »
He could propose to take 32 coins for himself and offer 34 each to 2 members of his crew. Content enough that no one will receive any more than them, those 2 should vote in his favour. The captain himself will vote in favour as well, giving a total of 3 votes, enough to save his life.

#### SquarishTriangle

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« Reply #108 on: 23/11/2008 04:47:52 »
On second thoughts, take 33 coins and offer 33 to 2 others, and 1 coin to split between the other 2. Same result.

#### lyner

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« Reply #109 on: 23/11/2008 13:11:06 »
The problem is that the two crew members he would hope to support him could probably do better by rejecting the offer.
I suggest that there would be no objection from his two 'supporters' if he offered them a lot more.
If he offered them 33 each and kept 34 for himself, they couldn't expect more than that so they would be bound to support him.
BUT there is probably a smarter answer which would give him more in the end.
If they go to the  'next round' after a mutiny, the new boss would still need to pay out to two others for a majority and he might not choose one of the original two. So they would possibly settle for a smaller cut.  But, how to work it out???

#### dentstudent

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« Reply #110 on: 25/11/2008 13:31:25 »
FROG - 28 days. After 27 days, he has reached 27 metres. On the 28th day, he can jump the final 3 metres and reach the top. This assumes that his first jump is on day 1, not day 0.

#### dentstudent

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« Reply #111 on: 25/11/2008 13:39:55 »
Socks: 3.

The options:

A) pick 1: B   pick 2: B              ==> B pair
B) pick 1: B   pick 2: W   pick 3: B  ==> B pair
C) pick 1: B   pick 2: W   pick 3: W  ==> W pair
D) pick 1: W   pick 2: W              ==> W pair
E) pick 1: W   pick 2: B   pick 3: B  ==> B pair
E) pick 1: W   pick 2: B   pick 3: W  ==> W pair

#### dentstudent

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« Reply #112 on: 25/11/2008 13:41:57 »
4th Child: Mary

#### dentstudent

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« Reply #113 on: 25/11/2008 13:47:56 »
pirates:

Could it be that the captain can retain 98 coins, with 2 other pirates each having 1 making 100. The other 2 pirates who don't get a coin won't agree, but since they are in the minority, they won't mutiny.

#### dentstudent

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« Reply #114 on: 25/11/2008 14:12:26 »
A sample of 100 kg of potatoes has a water content of 99%. It is put under the sun to dry a little, and the water content at the end becomes 98%. How does the potatoes weight now?

So 100 kg pots = 99% water plus 1% "stuff".

Therefore 1% stuff = 1kg and 99% water = 99kg.
98% water = 98 kg.
Pots = 1kg "stuff" plus 98kg = 99kg.

???

#### lyner

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« Reply #115 on: 25/11/2008 17:24:44 »
Can the captain rely on the two accepting the one coin each? All four crew could vote against him. Deal or No Deal demonstrates that people will reject a small prize if a larger one is still available- even if there is a chance of no prize.

#### lightarrow

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« Reply #116 on: 25/11/2008 19:57:43 »
A sample of 100 kg of potatoes has a water content of 99%. It is put under the sun to dry a little, and the water content at the end becomes 98%. How does the potatoes weight now?

So 100 kg pots = 99% water plus 1% "stuff".

Therefore 1% stuff = 1kg and 99% water = 99kg.
98% water = 98 kg.
Pots = 1kg "stuff" plus 98kg = 99kg.

???
No.
Hint: "to dry a little" means that the water content goes from 99% to 98%, not that the weight they lose is little...
When you will know the solution you will be surprised.

#### Bikerman

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« Reply #117 on: 25/11/2008 20:16:20 »
OK..99% water means 1% "stuff".
Now, afterwards we have 2% "stuff".

OK. if 2%=1kg then the total = 1/0.02 = 50kg.