Solve Enjoyable Enigmas with Mr.E's Challenge

[zoobyshoe]

Answer:
http://en.wikipedia.org/wiki/Functional_fixedness#Two-cord_problem

Interesting article.

For each object, you need to decouple its function from its form. McCaffrey (2012) shows a highly effective technique for doing so. As you break an object into its parts, ask yourself two questions. "Can I subdivide the current part further?" If yes, do so. "Does my current description imply a use?" If yes, create a more generic description involving its shape and material. For example, initially I divide a candle into its parts: wick and wax. The word 'wick' implies a use: burning to emit light. So, describe it more generically as a string. This brings to mind using the wick to tie things together (once I extract it from the wax). Since 'string' implies a use, I describe it more generically: interwoven fibrous strands. This brings to mind that I could use the wick to make a wig for my hamster. Since "interwoven fibrous strands" does not imply a use, I can stop working on wick and start working on wax. People trained in this technique solved 67% more problems that suffered from functional fixedness than a control group. This techniques systematically strips away all the layers of associated uses from an object and its parts.

A person whose prepared to deal with a balding hamster is prepared to deal with anything.

 

[drizzle]

You already answered it...

Another psych enigma
You are given 2 cords hanging from the ceiling, and a plier. You must connect the cords, but they are just far enough apart that one cannot reach the other easily.

Stupid me. I assumed they can never reach each other.

 

[zoobyshoe]

Herman, the hermit, spent his days walking the hills and dales, doing math in his head. Every day his walk was interrupted by a wide, shallow river. He had to bundle his clothes and lash them to the end of his walking stick, holding them above his head, while he walked across in water up to his neck. He dreamed of building a bridge.

There was, in fact, a tall tree growing right at the water's edge. Herman wondered if the tree were long enough to span the river. If it were, he could cut it down and walk across the tree everyday. Herman, though, had gone into hermitry with no dedicated measuring tools, or rope. He didn't know how wide the river was or how tall the tree.

One day he happened to arrive at the river at such a time of day that the tree's shadow reached just to the bank on the other side, cutting the river perpendicularly.

How could Herman use this fact to measure the tree and the river?

 

[Enigman]

Spoiler

Shadow of the stick should be shorter or of equal length to the stick itself. Similar triangles.

 

[Jonathan Scott]

How could Herman use this fact to measure the tree and the river?

Can he use this fact AND his walking stick?

 

[Jonathan Scott]

Can he use this fact AND his walking stick?

Spoiler

OK, I've now understood that Enigman had already got there, in that it seemed obvious to me to measure the ratio of the length of any other vertical object, such as a walking stick, to the length of its shadow, and knowing that I now understand what Enigman was saying, which got a little garbled!

 

[Enigman]

Migraine +coffee+ thermodynamic tables=gibberish

 

[zoobyshoe]

Both right!

Herman needs to quickly mark off the length of the shadow of his walking stick on the ground when the stick is held vertically. He could do that by placing a pebble at the base and tip of the shadow. Then he would need to lay the stick down along this line segment. If the pebbles are further apart than his stick is long, then the tree is too short to span the river. He doesn't even need an exact ratio.

 

[zoobyshoe]

Torty the tortoise lives around the corner from me. He's about 29cm long, nose to tail-end. One day as I was passing by I observed he was in motion. Fortunately I happened to have a Tortoise Speed Radar Gun with me. I pulled it from my backpack and clocked Torty moving at 10 furlongs per fortnight.

Which scenario might best explain this speed:

a.)Torty had been having an affair with the neighbor tortoise's wife. He'd just heard them arguing and knew the neighbor was after him. He was running for his life.

b.)Torty had been having an affair with the neighbor tortoise's wife. He'd just heard them arguing and knew the neighbor was after him. He was running for his life. Unfortunately, he and the neighbor's wife had downed 2 bottles of champagne the night before, and Torty was very hung over.

 

[Enigman]

How good a drinker is our adventuress (adventoise?)?

 

[zoobyshoe]

How good a drinker is our adventuress (adventoise?)?

In that scenario, they had a bottle each.

 

[Enigman]

Spoiler

I am going with a. A fight while having a hangover can't be too much fun.

 

[lendav_rott]

2km over 2 weeks makes the average speed like 0.0017 m/s, i think the tortoise had a little too much to drink at the time. Waay too drunk to be messing around with someone's wife in that condition

 

[ViperSRT3g]

I've been watching this thread all day and have become impatient at waiting for the last puzzle to be confirmed. So I'm posting this puzzle to see if anyone can solve it. (Be sure to make your guesses in spoiler tags!)

What is the next line in this series?
1
11
21
1211
111221

 

[collinsmark]

Torty the tortoise lives around the corner from me. He's about 29cm long, nose to tail-end. One day as I was passing by I observed he was in motion. Fortunately I happened to have a Tortoise Speed Radar Gun with me. I pulled it from my backpack and clocked Torty moving at 10 furlongs per fortnight.

Which scenario might best explain this speed:

a.)Torty had been having an affair with the neighbor tortoise's wife. He'd just heard them arguing and knew the neighbor was after him. He was running for his life.

b.)Torty had been having an affair with the neighbor tortoise's wife. He'd just heard them arguing and knew the neighbor was after him. He was running for his life. Unfortunately, he and the neighbor's wife had downed 2 bottles of champagne the night before, and Torty was very hung over.

Spoiler

Unless I missed something, scenario (b.) is identical to scenario (a.), word-for-word even, except with additional information. Invoking Occam's razor, scenario (a.) should be selected, since it makes the fewest assumptions [of the two choices].

 

[Enigman]

Ooo...smart.

 

[zoobyshoe]

2km over 2 weeks makes the average speed like 0.0017 m/s, i think the tortoise had a little too much to drink at the time. Waay too drunk to be messing around with someone's wife in that condition

This is correct. Torty's speed is not very fast, even for a tortoise. He's only going about 9.98 cm per minute, or 1.66mm per second. A sober snail in good shape could pass him.

Although he's in fear of his life in both scenarios, in the second he is terribly hung over and can't get out of first gear, so to speak.

 

[zoobyshoe]

Spoiler

Unless I missed something, scenario (b.) is identical to scenario (a.), word-for-word even, except with additional information. Invoking Occam's razor, scenario (a.) should be selected, since it makes the fewest assumptions [of the two choices].

The second scenario does not explicate the first. It contains a complication that doesn't exist in the first. If the first were true, we'd expect Torty to be moving very much faster. The only explanation for why a tortoise in fear of his life should be moving so slowly is offered in the second scenario.

 

[collinsmark]

The second scenario does not explicate the first. It contains a complication that doesn't exist in the first. If the first were true, we'd expect Torty to be moving very much faster. The only explanation for why a tortoise in fear of his life should be moving so slowly is offered in the second scenario.

Spoiler

That thought had crossed my mind. Ten furlongs per fortnight (less than 2 millimeters per second) is very slow for a tortoise. That's even slow for a snail.

On the other hand, the riddle does put us in a peculiar universe where tortoises have extramarital affairs and quaff bottles of champagne. It's hard for me to imagine how slow a speed, or the cause of the slowness, would constitute out-of-the-ordinary in such a universe.

 

[collinsmark]

I've been watching this thread all day and have become impatient at waiting for the last puzzle to be confirmed. So I'm posting this puzzle to see if anyone can solve it. (Be sure to make your guesses in spoiler tags!)

What is the next line in this series?
1
11
21
1211
111221

Spoiler

I think I might have it, maybe. If so, this is my guess: 312211

The rule for generating the next number is to describe the number of consecutive digits in the present number (starting the most significant digits) and state those digits. Remove all punctuation and non-number words. Start with '1'.

1
So the next number is the numerical version of the statement,
One '1' ==> 11
The next number is the numerical version of the statement,
Two '1's == > 21
The next number is the numerical version of the statement,
One '2' and one '1' ==> 1211
The next number is,
One '1', one '2', and two '1's ==> 111221

Which brings us to the answer,
Three '1's, two '2's, and one 1 ==> 312211

 

[zoobyshoe]

Spoiler

That thought had crossed my mind. Ten furlongs per fortnight (less than 2 millimeters per second) is very slow for a tortoise. That's even slow for a snail.

On the other hand, the riddle does put us in a peculiar universe where tortoises have extramarital affairs and quaff bottles of champagne. It's hard for me to imagine how slow a speed, or the cause of the slowness, would constitute out-of-the-ordinary in such a universe.

The point, as with most word problems, is to cut to the quick of the narrative and determine what's being asked. Here the problem is simply to figure out if "10 furlongs per fortnight" is fast or slow for a tortoise. The particular reasons offered that the tortoise might be going faster or slower than he otherwise would are merely entertaining and decorative mud intended to slow you down in penetrating to the core problem.

 

[ViperSRT3g]

Spoiler

I think I might have it, maybe. If so, this is my guess: 312211

The rule for generating the next number is to describe the number of consecutive digits in the present number (starting the most significant digits) and state those digits. Remove all punctuation and non-number words. Start with '1'.

1
So the next number is the numerical version of the statement,
One '1' ==> 11
The next number is the numerical version of the statement,
Two '1's == > 21
The next number is the numerical version of the statement,
One '2' and one '1' ==> 1211
The next number is,
One '1', one '2', and two '1's ==> 111221

Which brings us to the answer,
Three '1's, two '2's, and one 1 ==> 312211

Correct! And I thought that would stump some people :[

 

[collinsmark]

Correct! And I thought that would stump some people :[

It almost did! I started out ...

Spoiler

... assuming the numbers were in ternary (base 3), converted them to decimal, then got a whole lot of nowhere. The sentence translation thing was mostly stumbling luck right before I was about to give up.

 

[zoobyshoe]

It almost did! I started out ...

Spoiler

... assuming the numbers were in ternary (base 3), converted them to decimal, then got a whole lot of nowhere. The sentence translation thing was mostly stumbling luck right before I was about to give up.

Spoiler

Good job getting the right answer! I also started following the base 3 red herring, then just gave up.

 

[zoobyshoe]

I went to a certain FF Restaurant last night and when I was given my order number I noticed it was 411. I thought, "That's an odd number!," and decided to see if it was prime. It turns out to be the product of 3*137.

And that's the 411 on 411.

211,311,811,911 are prime, but
111,411,511,611,711,1011 are composite. 711 is the odd man out, having three factors. All the others have two.

These are interesting:

111 = 3*37
411 = 3*137
711 = 3*237 (but unlike the others, 237 is not prime.)
1011=3*337, etc.


None of the '11' composites thus far have 11 as a factor. The first composite '11' number to have 11 as a factor is: 1111. What is the last? Is there some number ending in 11 having 11 as a factor larger than which there can be no others with those features? If not, then we have the theorem: There is an infinite number of numbers ending in 11 having 11 as a factor. When you finish this sentence you have 30 seconds to prove the theorem.

 

[Enigman]

Spoiler

1100n+11

 

[zoobyshoe]

Spoiler

1100n+11

Spoiler

Q.E.D. But I was just about sure someone would prove it by proving it for all numbers: The number of numbers, n, ending in n, having n as a factor, is infinite.

Spoiler

(Not sure I phrased that right.)

 

[Enigman]

100xn+x?

 

[zoobyshoe]

100xn+x?

Spoiler

The way you generate one is pick any number and precede it by itself or a multiple of itself (works for single digits, any number of digits). Since an infinite number of multiples of any number is possible, there will be an infinite number of numbers that fit the criteria (ending in n and having n as a factor).

 

[Cowpoke]

I would guess that the Princess is not stationery, therefore she may choose which of the suitors to approach.

 

[Enigman]

See if you can get what's going on before the end of the video:

 

[Psinter]

See if you can get what's going on before the end of the video:

I thought it was a flat piece of paper with perspective drawings, but I was wrong.

I don't have an answer to all of them. I got 9 of them:

1, 2, 6, 7, 8, 9, 11, 12, 14

If you guess those you win (because I only have an answer to those).

(Number 4 is puzzling me, looks like some sort of series or sequence)

 

[Travis_King]

I thought it was a flat piece of paper with perspective drawings, but I was wrong.

I don't have an answer to all of them. I got 9 of them:

1, 2, 6, 7, 8, 9, 11, 12, 14

If you guess those you win (because I only have an answer to those).

(Number 4 is puzzling me, looks like some sort of series or sequence)

So, 3 is:

Spoiler

Signs

4 is:

Spoiler

Mean Girls

5 is:

Spoiler

Sum of All Fears

I think 13 is:

Spoiler

XXX (w/ Vin Deisel)

15 should be:

Spoiler

Speed

16 is:

Spoiler

127 Hours

I don't know what 10 is...I have an idea, but it doesn't seem even close

 

[Psinter]

So, 3 is:

Spoiler

Signs

4 is:

Spoiler

Mean Girls

5 is:

Spoiler

Sum of All Fears

I think 13 is:

Spoiler

XXX (w/ Vin Deisel)

15 should be:

Spoiler

Speed

16 is:

Spoiler

127 Hours

I don't know what 10 is...I have an idea, but it doesn't seem even close

Awesome! It was supposed to be the other ones, but since you got those even better. To think number 4 was "mean".

Number 10 sounds like Iron Man, but I see no man anywhere. So nope.

 

[collinsmark]

I thought it was a flat piece of paper with perspective drawings, but I was wrong.

I don't have an answer to all of them. I got 9 of them:

1, 2, 6, 7, 8, 9, 11, 12, 14

If you guess those you win (because I only have an answer to those).

(Number 4 is puzzling me, looks like some sort of series or sequence)

Number 2 is

Spoiler

The Matrix

Number 6 is

Spoiler

Snakes on a Plane

Number 8 is

Spoiler

Alpha and Omega

Number 9 is

Spoiler

The Exorcist

Number 12 is

Spoiler

Vertical Limit

Number 14 is

Spoiler

E

So that still leaves
1, 7, 10, 11 and 13.

[Edit:
Number 1 might be

Spoiler

Sin City

but I'm not 100% on that.]