Solve Enjoyable Enigmas with Mr.E's Challenge

[lisab]

Spoiler

Bend the straw so it's like an L, stick it in the bottle and try to wedge it in the neck, and lift.

 

[Enigman]

Spoiler

Bend the straw so it's like an L, stick it in the bottle and try to wedge it in the neck, and lift.

You got it!

 

[Enigman]

Now stick the straw into a potato: It generally bends when you poke it...so what do you do?
(I seem to remember something about random opinions and Lisab's potatoes...)

 

[zoobyshoe]

This one needs a diagram (attached):

"The magic numbers for the wheel of fortune are: 34, 42, 43, 50, 51, 52, 59, 60, and 68. Place each of these numbers in the proper circle so that:

1. The three numbers on each straight line equal 153.

2. The numbers in circles ABC, CDE, EFG, and GHA also equal 153.

We have placed the number 59 in a circle to get you started."

No computers allowed!

 

[collinsmark]

This one needs a diagram (attached):

"The magic numbers for the wheel of fortune are: 34, 42, 43, 50, 51, 52, 59, 60, and 68. Place each of these numbers in the proper circle so that:

1. The three numbers on each straight line equal 153.

2. The numbers in circles ABC, CDE, EFG, and GHA also equal 153.

We have placed the number 59 in a circle to get you started."

No computers allowed!

Spoiler

Solved it!

But I won't give it away just yet. It's a pretty rewarding puzzle and I don't want to completely spoil it so soon.

But here are some hints in case you are stuck. (*partial spoiler warning*)

(i) There are two solutions to this puzzle. Each solution is a mirror image of the other along the G-<center>-C axis.
(ii) Process of elimination is involved, but choose smartly. It's not too hard to group each number into one of three categories: (a) on the top, bottom, or right, (b) along a diagonal [but not at center], or (c) center.
(iii) Once you find the only number that can be in the center, you get the number to the right as a freebie, extra special bonus.
(iv) When you find a number that can be either at the top or bottom (but not right), just pick one. Remember from (i) that there are two symmetrical solutions. So just pick one or the other, top or bottom; it doesn't matter.

 

[Enigman]

[STRIKE]Work in progress:[/STRIKE] DONE!
34, 42, 43, 50, 51, 52, 59, 60, and 68

Spoiler

Average value: 51
Diameters:
59, 51, 43
60, 51, 42
68, 51, 34
50, 51, 52
...60
...34...50
59...51...43
...52...68...
...42....

Sectors:
with 59: 60,59,34 ; 42,59,52
with 60: 60,59,34 ; 43,60,50
59 and 60 both belong to two sectors

 

[Enigman]

Now stick a straw into a potato: It generally bends when you poke it...so what do you do?
(I seem to remember something about random opinions and Lisab's potatoes...)

...

 

[zoobyshoe]

You both got it. I don't know about you, but the only way I could see to approach it was to do a lot of tedious subtraction from 153. Eventually I figured out 51 was the only option for the center, then the rest was easier.

 

[Enigman]

You both got it. I don't know about you, but the only way I could see to approach it was to do a lot of tedious subtraction from 153. Eventually I figured out 51 was the only option for the center, then the rest was easier.

Well, the center no. had to be there in all the summations, so it would'nt be too big or too small and averaging out all the numbers would give us a rough idea about where the number is.
The average comes out to be 51...which was lucky, I expected decimals...
So 153-51=102 I just went on subtracting the numbers from 102 to see if the remainder was in the list. Luckily it was, otherwise I would have to check with 50 and 52 depending on the remainder <rinse and repeat>

 

[consciousness]

Now stick the straw into a potato: It generally bends when you poke it...so what do you do?
(I seem to remember something about random opinions and Lisab's potatoes...)

Some possible answers-

Spoiler

Cut/bend the straw so that a small segment of it is in your hand. Now push hard (it won't bend as the segment is too small). Alternatively boil the potato to make it soft.

 

[Enigman]

Some possible answers-

Spoiler

Cut/bend the straw so that a small segment of it is in your hand. Now push hard (it won't bend as the segment is too small). Alternatively boil the potato to make it soft.

No damage either to potato or straw would be nice...
(Menu this evening: Coke and chips)

 

[Enigman]

Now stick the straw into a potato: It generally bends when you poke it...so what do you do?
(I seem to remember something about random opinions and Lisab's potatoes...)

Hint:

Spoiler

It won't work with a straw that has a hole in it

 

[AlephZero]

I don't know about you, but the only way I could see to approach it was to do a lot of tedious subtraction from 153.

Not so much "tedious subtraction" as "counting on your fingers" once you get a start.

Look at the differences between the numbers

34 42 43 50 51 52 59 60 68
  8  1  7  1  1  7  1  8

Symmetrical, no? You need four sets of three containing the same number (to go in the center), and they are
34 51 68
42 51 60
43 51 59
50 51 52

You also need three sets containing 59, and the options are
59 51 43 (you got that one already)
59 52 42
59 60 34
You need two of the four numbers 52 42 60 34 to make a line across the center with 51, and the only possibility (from the first list) is 42 and 60.

Now, fill in the diagram

 

[zoobyshoe]

Not so much "tedious subtraction" as "counting on your fingers" once you get a start.

Look at the differences between the numbers

34 42 43 50 51 52 59 60 68
  8  1  7  1  1  7  1  8

Symmetrical, no? You need four sets of three containing the same number (to go in the center), and they are
34 51 68
42 51 60
43 51 59
50 51 52

You also need three sets containing 59, and the options are
59 51 43 (you got that one already)
59 52 42
59 60 34
You need two of the four numbers 52 42 60 34 to make a line across the center with 51, and the only possibility (from the first list) is 42 and 60.

Now, fill in the diagram

Despite having solved the puzzle, I had a strong suspicion my method was the crudest, and that there had to be a more intelligent approach. I did not naturally notice the symmetry around 51 you point out here, but that would have been the needed insight to a very fast solution.

Now that I see the symmetry, I suspect it is necessary for the puzzle to work as it does. If we were to design a similar puzzle summing to a different number, the choices would have also to be symmetrically arranged around the center number.

 

[Enigman]

Now stick the straw into a potato: It generally bends when you poke it...so what do you do?

Spoiler

Think eggs and bottles...https://www.physicsforums.com/showpost.php?p=4516938&postcount=305

 

[consciousness]

Hint:

Spoiler

It won't work with a straw that has a hole in it

Hmm this might work-

Spoiler

Light a matchstick and station the straw directly above it. This should create a a low pressure region inside the straw and it might collapse into a strip, making the job easy.

 

[Enigman]

Hmm this might work-

Spoiler

Light a matchstick and station the straw directly above it. This should create a a low pressure region inside the straw and it might collapse into a strip, making the job easy.

No the heat's going to make it more squishy...we need it to stop bending...keep thinking air pressure.

 

[zoobyshoe]

No the heat's going to make it more squishy...we need it to stop bending...keep thinking air pressure.

Spoiler

Are you suggesting blowing into one end of the straw while you try and push the other end into the spud?

 

[collinsmark]

Now stick the straw into a potato: It generally bends when you poke it...so what do you do?

Hmm.

Spoiler

This might work, maybe. It reminds me of a trick one can use to make a straw pop pretty loud when snapped with a finger (that process destroys the straw). Anyway, here's a modification of that, that might instead work for this one.

But I have not tried this due to temporary lack of straws and potatoes. It's just a guess.

o Take the straw and bend it in the middle.
o Twist each end around so there is a noticeable, sharp, bend/twist thing around in the middle. Be careful though, you don't want to twist so much that it compromises the straw's integrity.
o Keeping the twist in place, hold one end of the straw between a pair of fingers or between a finger and thumb (the finger and thumb is probably easier).
o Do the same with the the other end of the straw and the other hand.
o Pinch both ends of the straw at all times.
o Move both hands in a circular motion with a axis parallel to left and right. The goal is to place twists on both ends of the straw to trap the air inside. If done right, you should be able to feel the straw bulge a little bit in the middle parts, due to the trapped air.
o Don't twist so much that the straw bursts though. Just inflate it enough so it resists bending.
o Bring your hands together, causing the inflated parts of the straw to bend in half. Now there are two inflated parts of the straw with a sharp bend in the middle.
o Use the sharp bend in the middle to impale the potato. This might take a bit of a balancing act to keep the potato from rolling out from under the straw. It also might require chipping/drilling away at the potato skin at first, perhaps with the sharper "bend" in the straw, just to get a divot going that can then be used to ease the process potato goring.
o Once the straw has sufficiently skewered the potato, perhaps it will hold tight enough to lift the potato?

 

[zoobyshoe]

"Each horizontal row in the grid has the same mathematical relationship. If you can identify the pattern, you will be able to supply the missing numbers in the bottom row."

 

[AlephZero]

Too easy, for us oldies who learned to do arithmetic before there were calculators.

Spoiler

24, in base 7. But the answer is in base 10 of course.

 

[zoobyshoe]

I fit that description, and it took a long time before I saw it. You're just very number-minded.

 

[zoobyshoe]

Even easier, but I found it fun:

Magic Nines

"Each digit from 1 to 9 is used only once. The first and second row of digits are added to obtain the sum in the bottom row.

Rearrange these digits in seven similar boxes so that the sum increases each time by nine. More than one solution is possible."

(I suggest putting lower digits on top.)

 

[Enigman]

Spoiler

Are you suggesting blowing into one end of the straw while you try and push the other end into the spud?

That would work...

Hmm.

Spoiler

This might work, maybe. It reminds me of a trick one can use to make a straw pop pretty loud when snapped with a finger (that process destroys the straw). Anyway, here's a modification of that, that might instead work for this one.

But I have not tried this due to temporary lack of straws and potatoes. It's just a guess.

o Take the straw and bend it in the middle.
o Twist each end around so there is a noticeable, sharp, bend/twist thing around in the middle. Be careful though, you don't want to twist so much that it compromises the straw's integrity.
o Keeping the twist in place, hold one end of the straw between a pair of fingers or between a finger and thumb (the finger and thumb is probably easier).
o Do the same with the the other end of the straw and the other hand.
o Pinch both ends of the straw at all times.
o Move both hands in a circular motion with a axis parallel to left and right. The goal is to place twists on both ends of the straw to trap the air inside. If done right, you should be able to feel the straw bulge a little bit in the middle parts, due to the trapped air.
o Don't twist so much that the straw bursts though. Just inflate it enough so it resists bending.
o Bring your hands together, causing the inflated parts of the straw to bend in half. Now there are two inflated parts of the straw with a sharp bend in the middle.
o Use the sharp bend in the middle to impale the potato. This might take a bit of a balancing act to keep the potato from rolling out from under the straw. It also might require chipping/drilling away at the potato skin at first, perhaps with the sharper "bend" in the straw, just to get a divot going that can then be used to ease the process potato goring.
o Once the straw has sufficiently skewered the potato, perhaps it will hold tight enough to lift the potato?

may work but wholly unnecessary...

https://www.youtube.com/watch?v=8Ewpwylbxec

 

[consciousness]

Monks With Eye Problems PART 2-

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide.

These monks will believe anything others say, as long as it isn't certain that they are lying.

Then one day a greedy and evil logician comes to the island. He recognizes that this system is very unstable and decides to take advantage of it. He wants the entire island to himself, but he knows that if he speaks an obvious lie the monks will kill him.

Think of a statement he can make to get all of the monks on the island to kill themselves as quickly as possible.
-------------------------------
This is much harder than the first because there we had to find the consequences of a statement while here we have to make the statement. I suggest trying the first one before this(its on page 35).

 

[zoobyshoe]

That would work...

Probably not, now that I see how it's done. You need some momentum.

 

[consciousness]

Monks With Eye Problems PART 2-

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide.

These monks will believe anything others say, as long as it isn't certain that they are lying.

Then one day a greedy and evil logician comes to the island. He recognizes that this system is very unstable and decides to take advantage of it. He wants the entire island to himself, but he knows that if he speaks an obvious lie the monks will kill him.

Think of a statement he can make to get all of the monks on the island to kill themselves as quickly as possible.
-------------------------------
This is much harder than the first because there we had to find the consequences of a statement while here we have to make the statement. I suggest trying the first one before this(its on page 35).

Clarification- The logician can go away making the statement and come back later to find an empty island. The main thing is that the monks shouldn't immediately realize that he was lying.

 

[consciousness]

This is too hard so I will provide some help.

How to start with the problem-

Spoiler

Suppose that there are n Red Eyed Monks(REM) and m Blue Eyed Monks(BEM).

Now, every REM knows that there are either (n-1) or n REMs and correspondingly m or (m+1) BEMs.
Every BEM knows that there are either m or (m-1) BEMs and correspondingly n or (n+1) REMs.

How to proceed with it-

Spoiler

The tricky part is to convince a BEM that he is a REM without saying an obvious lie. In most solutions a REM can infer that he is a REM when a BEM kills himself.

There two ways to do this- Imply that there are (m-1) BEMs or that there are (n+1) REMs.

We have to imply it in such a way that REMs can't immediately know that we are lying.

For example- "There are (m-1) BEMs" and "There are (n+1) REMs" don't work.

Now all you need is a stroke of insight!

 

[consciousness]

Did I kill this thread?

The answer was-

Spoiler

"The number of REMs is odd" if n is even or "The number of REMs is even" if n is odd. Similar thing with the number of BEMs also works.

 

[Enigman]

Hang on or Let Go?

A painter (you) is high up on a ladder, painting a house, when unfortunately the ladder starts to fall over from the vertical. What to do:
let go of the ladder right away and fall to the ground, or hang on to the ladder all the way to the ground?

 

[zoobyshoe]

A painter (you) is high up on a ladder, painting a house, when unfortunately the ladder starts to fall over from the vertical. What to do:
let go of the ladder right away and fall to the ground, or hang on to the ladder all the way to the ground?

Spoiler

Under the circumstances, the tip of the ladder will be going faster than the velocity of its center of gravity when it hits the ground. So, your best bet is to let go.

Spoiler

On the other hand, I just realized that you holding onto the ladder creates a thing with a different center of gravity than the ladder alone, so I'm not sure which way gets you injured less.

 

[Enigman]

Spoiler

Under the circumstances, the tip of the ladder will be going faster than the velocity of its center of gravity when it hits the ground. So, your best bet is to let go.

Correct.
This was used in a psychological study:
You are given with the following task: how to fix a lit candle on a wall (a cork board) in a way so the candle wax won't drip onto the table below. To do so, one may only use the following along with the candle:

1. a book of matches
2. a box of thumbtacks

 

[zoobyshoe]

Correct.

Only if you are massless, I think. See my second spoiler above.

Spoiler

Edit after more thinking: Yes, by holding onto the ladder you are shifting its (the human-ladder system's) COG up and retarding the descent of the tip. The ladder, though, is shifting your COG down, such that it is still slightly better to let go of it.

 

[Enigman]

Oh dear, did I give my answer away too soon?

Spoiler

The total impact energy is going to be the potential energy at the start. So either you absorb the impact of both masses or just one mass. The most elegant solution however is to try and slide down the ladder reducing the impact to minimal

 

[drizzle]

Correct.
This was used in a psychological study:
You are given with the following task: how to fix a lit candle on a wall (a cork board) in a way so the candle wax won't drip onto the table below. To do so, one may only use the following along with the candle:

1. a book of matches
2. a box of thumbtacks

Psychological study you say... Now I'm afraid to give my answer.

Spoiler

Pin the candle totally perpendicular to the wall using the thumbtacks and then lit it. Oh just do it under the table surface' level, so the wax won't drip on it.

 

[Enigman]

Psychological study you say... Now I'm afraid to give my answer.

Spoiler

Pin the candle totally perpendicular to the wall using the thumbtacks and then lit it. Oh just do it under the table surface' level, so the wax won't drip on it.

Won't work, wax is too soft and the candle will just fall down, roll towards the legs of the table and set the table on fire.

 

[drizzle]

Won't work, wax is too soft and the candle will just fall down, roll towards the legs of the table and set the table on fire.

Spoiler

Fine then, use the matches to form two words 'LIT CANDLE' and pin them on the wall using the thumbtacks.

 

[zoobyshoe]

Didn't you already post this candle enigma?

 

[drizzle]

Did he?... *checks the previous enigmas*

 

[zoobyshoe]

It seems familiar, but I can't find it. Anyway...

Spoiler

If the thumb tack box were suitably shaped, I would try pinning it to the corkboard from the inside, sticking out like a little shelf, and put the candle on it.

 

[drizzle]

I KNEW the box thing has to do something here.

 

[Enigman]

Didn't you already post this candle enigma?

Nope, but it's pretty popular with self-help authors.

Follow these steps and see if you can figure this out.

1) Get a brown, cardboard box.
2) Get purple, orange, and turquoise paints.
3) Paint the box orange.
4) Paint on purple spots.
5) Paint on turquoise stripes.
7) Turn it upside down.
8) Lie on your side.

What is missing from this sequence?

 

[zoobyshoe]

What is missing from this sequence?

Spoiler

Step # 6

 

[zoobyshoe]

Here's what I was saying about the ladder:

Video:
[Youtube]BV7TPvk__kE[/youtube]

Explanation:

http://www.darylscience.com/Demos/Faster g.html

Get a film clip of a falling industrial chimney. This is the explanation of why they snap in half BEFORE they hit the ground. At the chimney begine to topple over, it's center of mass accelerates at 10m/s2. This, however, tries to force the TOP of the chimney to accelerate FASTER than 'g'! This causes tremendous strain on the structure and it crumbles on the way down. Cool!

 

[Jonathan Scott]

Oh dear, did I give my answer away too soon?

Spoiler

The total impact energy is going to be the potential energy at the start. So either you absorb the impact of both masses or just one mass. The most elegant solution however is to try and slide down the ladder reducing the impact to minimal

Yep, I can confirm that sometimes works!

 

[zoobyshoe]

Follow these steps and see if you can figure this out.

1) Get a brown, cardboard box.
2) Get purple, orange, and turquoise paints.
3) Paint the box orange.
4) Paint on purple spots.
5) Paint on turquoise stripes.
7) Turn it upside down.
8) Lie on your side.

What is missing from this sequence?

After two days I still haven't the faintest idea. Need a clue.

 

[Enigman]

After two days I still haven't the faintest idea. Need a clue.

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.

 

[zoobyshoe]

You already answered it...

WOW! I was authentically just being a wise-***!

You must confirm or deny, or no one really knows what sort of answer is required.

 

[zoobyshoe]

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.

I have seen this one before, so I'll recuse myself. I bet Gad can answer this one.

 

[drizzle]

I have seen this one before, so I'll recuse myself. I bet Gad can answer this one.

Spoiler

Cut the cords with the plier then tie them together?