Solve Enjoyable Enigmas with Mr.E's Challenge

[Enigman]

The problem statement is all you get.

(Okay, a leetle bit of advice: Do not stay in the box, stay and your fate's as uncertain as the cat's and I do love killing that particular variety of cat...I am a curious person)

 

[Travis_King]

Spoiler

I want to say that it's not possible to dig half a hole. Once you break dirt you've got yourself a whole hole!

 

[Enigman]

Spoiler

I want to say that it's not possible to dig half a hole. Once you break dirt you've got yourself a whole hole!

Well said!

 

[Travis_King]

Here's a pretty easy one:

Two boys, Mikey and Jimmy are running a 100 meter foot-race. The first time they race Mikey beats Jimmy by 5 meters. To make things fair, the next time they race, Mikey stands 5 meters behind the starting line.

Assuming they each run just as fast as they did in the first race, does Jimmy win the second race?

 

[CompuChip]

Do we also assume they each run just as far as in the first race? :P

 

[AlephZero]

What is the maximum number of kings that can be placed on a chess board so that none of them threatens any other?

64, if they are all black or all white

 

[CompuChip]

64, if they are all black or all white

EDIT: A better way to put it would be maximum number of independent kings...

Hence the edit :P

 

[Enigman]

64, if they are all black or all white

That's why I included 'independent' in the edit.

Here's a pretty easy one:

Two boys, Mikey and Jimmy are running a 100 meter foot-race. The first time they race Mikey beats Jimmy by 5 meters. To make things fair, the next time they race, Mikey stands 5 meters behind the starting line.

Assuming they each run just as fast as they did in the first race, does Jimmy win the second race?

Spoiler

Let t be time taken by M
Vm-100/t velocity of M
Vj-95/t velocity of J
Now-
Tm=105/Vm
Tm=1.05t
Tj=100/Vj
Tj=1.053t
Tj>Tm
M wins

 

[Travis_King]

CompuChip - yup, you sure can.

That's it Enigman

Spoiler

some basic algebra for everyone!

How about this one:

A cashier tells you that the candybar you are trying to purchase costs $1.50. You hand him thirty five-cents. How much change do you get back?

 

[Enigman]

Spoiler

...0?

 

[Travis_King]

Spoiler

...0?

That's it

Spoiler

I enjoy the one's that are super easy once you understand the semantics haha

 

[Enigman]

“There are three kinds of lies: lies, damned lies, and statistics”
-JUST VENTING...

So a prisoner in Enigmania (small kingdom in wonderland - yeah I made that up) gets a death senence, King Enigmaniac follows the usual procedure before going OWHH on him:
Prisoner is brought in a room and is given a bag with five hundred black balls and five hundred white balls and two bowls the state wizard Enigmax then tells him to divide the balls and place them in the bowls in any ratio he wants provided all the balls are in the bowl, after which he would be blind-folded and asked to pick a ball from a bowl randomly chosen. White he lives black Enigmaniac gets to yell OWHH (Off With His Head) the prisoner would rather not lose his head(- Wonderland already has many headless fools tottering about... not to mention that grin without a cat...) Ah well, what should the prisoner do to keep his head that is except keeping his head?
[Pardon the jabberwock...did I mention I hate probabilities?]

 

[zoobyshoe]

You're saying all the black balls in one bowl, and white ones in the other?

 

[Enigman]

You're saying all the black balls in one bowl, and white ones in the other?

Colours don't matter as long as all balls are in bowls.
(A misplaced vowel E in the sentence might make it vulgar...)

Given all balls are indeed in the bowls you may do anything eg. 50 black and 50 white in one rest in the other

 

[CompuChip]

Spoiler

One good strategy would be: put one black ball in one bowl, and the rest in the other bowl. The probability that he keeps his head is 1/2 + 1/2 * 499 / 1000

This gives about 3/4 chance of his surviving; which is definitely more than the 1/2 you would get from a naive strategy. Question is if there is a way he can do even better. In particular I'm wondering if there is a guaranteed win strategy.

 

[Enigman]

Spoiler

One good strategy would be: put one black ball in one bowl, and the rest in the other bowl. The probability that he keeps his head is 1/2 + 1/2 * 499 / 1000

Bah, humbug! You have kept your head and if the prisoner is lucky he will too...

Question is if there is a way he can do even better. In particular I'm wondering if there is a guaranteed win strategy.

Enigmaniac is going to go OWTHH on you if you carry on your heretic ideas of freeing all prisoners and rendering a perfectly good system null...
(Jabberwock translation- That was the best strategy AFAIK)

 

[Enigman]

A farmer wants to make pens for his 9 pigs. Problem is that the pigs are quite clever and will escape from the pen if there are more than one in there by climbing on each others back. So he buys 28 planks to make the pens with one pig in each pen.
_______________
I_I_I_I_I_I_I_I_I_I

But the pigs steal four of the planks. What should the farmer do now?
_____________
I_I_I_I_I_I_I_I_ ... ??

 

[CompuChip]

I am tempted to say: "let them all go". But I like my head where it is.

PS I thought pigs only climb each others back for different reasons... I haven't seen them use it to escape.

 

[consciousness]

A farmer wants to make pens for his 9 pigs. Problem is that the pigs are quite clever and will escape from the pen if there are more than one in there by climbing on each others back. So he buys 28 planks to make the pens with one pig in each pen.
_______________
I_I_I_I_I_I_I_I_I_I

But the pigs steal four of the planks. What should the farmer do now?
_____________
I_I_I_I_I_I_I_I_ ... ??

Spoiler

Join the "open" end to the "closed" end to make a circle. This will result in 8 pens. But wait! An enclosed area is also created in the middle. So keep the thief pig there watched by 8 other pigs

 

[Enigman]

Spoiler

Join the "open" end to the "closed" end to make a circle. This will result in 8 pens. But wait! An enclosed area is also created in the middle. So keep the thief pig there watched by 8 other pigs

Done! Or should I say Sowld

Spoiler

_____
I_I_I_I
I_I_I_I
I_I_I_I

 

[Enigman]

A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up.

How can he divide the cards into two piles (possibly of different sizes) with each pile having the same number of cards facing up?

 

[Jonathan Scott]

A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up.

How can he divide the cards into two piles (possibly of different sizes) with each pile having the same number of cards facing up?

Spoiler

Take any 10 cards from the deck and turn them over to form one pile, with the rest of the deck forming the other pile.

 

[Office_Shredder]

Spoiler

Take any 10 cards from the deck and turn them over to form one pile, with the rest of the deck forming the other pile.

Witchcraft!

 

[zoobyshoe]

Spoiler

In particular I'm wondering if there is a guaranteed win strategy.

Spoiler

I should think he could make sure all the white balls are on top in both bowls, with black balls at the bottom.

 

[Office_Shredder]

“There are three kinds of lies: lies, damned lies, and statistics”
-JUST VENTING...

So a prisoner in Enigmania (small kingdom in wonderland - yeah I made that up) gets a death senence, King Enigmaniac follows the usual procedure before going OWHH on him:
Prisoner is brought in a room and is given a bag with five hundred black balls and five hundred white balls and two bowls the state wizard Enigmax then tells him to divide the balls and place them in the bowls in any ratio he wants provided all the balls are in the bowl, after which he would be blind-folded and asked to pick a ball from a bowl randomly chosen. White he lives black Enigmaniac gets to yell OWHH (Off With His Head) the prisoner would rather not lose his head(- Wonderland already has many headless fools tottering about... not to mention that grin without a cat...) Ah well, what should the prisoner do to keep his head that is except keeping his head?
[Pardon the jabberwock...did I mention I hate probabilities?]

This is probably the kind of cheating that would cause you get another "Off with your head" sentence upon doing in Wonderland.

Spoiler

The wizard told him to divide the balls. So cut the white balls up into like 1,000,000 balls, then put half the balls into each bowl and you have a pretty good shot of drawing a white one. You can even feel the size difference to guarantee it.

Alternatively, cut the black balls, at which point they are no longer balls. Place some white balls in each bowl, all the balls are in a bowl because the black objects are no longer balls, and draw your white ball and feel happy.

 

[collinsmark]

A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up.

How can he divide the cards into two piles (possibly of different sizes) with each pile having the same number of cards facing up?

Spoiler

Take any 10 cards from the deck and turn them over to form one pile, with the rest of the deck forming the other pile.

Oooh, I like that one. I'm kicking myself for not thinking of it on my own.

 

[Enigman]

Spoiler

Take any 10 cards from the deck and turn them over to form one pile, with the rest of the deck forming the other pile.

Correct!
I was trying to remember the russian for yes but nyet, no luck...
E

P.S Enigmaniac sends his regards with a few OWHH rain-checks for zoobie and O_S.
I expect the Hatter will be around to get the measurements for the funeral hats...mmm...you might still be saved- Enigmax asked the Hatter a riddle (No, not the difference between a raven and a writing desk...he answered that ages ago) if you solve it he probably will put a good word for you with that Maniac ...ahem, Enigmaniac.
the riddle-

I buried four fishermen up to their necks in the sand on the beach at low tide for keeping their fishing spot a secret from me. I put a hat on each of their heads and told them that one of them must shout out the correct color of their own hat or they will all be drowned by the incoming tide. I give them 10 minutes to do this. Fisherman A and B can only see the sand dune I erected. Fisherman C can see that fisherman B has a white hat on. Fisherman D can see that C has a black hat, and B has a white hat. The fisherman have been told that there are four hats, two white and two black, so they know that they must have either a white or a black hat on. who shouts out the color of their hat and how do they know?

 

[Enigman]

 

[drizzle]

Would ten minutes be enough for the tides to remove the sand dune?

 

[AlephZero]

Spoiler

If D sees C and B have the same color hats, he knows his hat is the other color.
If D doesn't shout, C knows his hat is the opposite color to B

If that was too easy, try the version for grown ups here: https://www.physicsforums.com/showthread.php?t=726180

 

[Enigman]

Spoiler

If D sees C and B have the same color hats, he knows his hat is the other color.
If D doesn't shout, C knows his hat is the opposite color to B

If that was too easy, try the version for grown ups here: https://www.physicsforums.com/showthread.php?t=726180

Zoobie keeps his head and O_S seems to have already shredded my Enigma... O_S gave another hat enigma a couple of pages back that one was great too...

 

[CompuChip]

Or how about the island where everyone kills themselves because a tourist comes along who likes blue eyes?

 

[Enigman]

Or how about the island where everyone kills themselves because a tourist comes along who likes blue eyes?

That was conciousness' enigma and had me quite befuddled...

Next One:
(And a classic one)
As I was going to St Ives,
I met a man with seven wives,
Every wife had seven sacks,
Every sack has seven cats,
Every cat has seven kits,
Kits, cats, sacks, and wives,
How many were going to St Ives?
-Mother Goose collection 18th century

 

[zoobyshoe]

Was the narrator going in the same direction as the man with seven wives?

 

[Enigman]

Spoiler

Was the narrator going in the same direction as the man with seven wives?

Nope.
Spoiler it.
The enigma was a variation of the Rhine papyrus puzzle (with some added trickery)- one of the world's oldest puzzles 1850 BC. But that was with 7 houses and other things... Rhine puzzle was primarily a calculative one.

 

[Enigman]

Place 5 pennies so that every penny touches every other penny.

 

[CompuChip]

Do I have to be the first again to come up with

Spoiler

$$\sum_{k = 0}^n 7^k = \frac{1 - 7^{n + 1}}{1 - 7}$$\

and start the discussion about the narrator himself (k = 0 or k = 1)? :P

 

[Enigman]

Do I have to be the first again to come up with

Spoiler

$$\sum_{k = 0}^n 7^k = \frac{1 - 7^{n + 1}}{1 - 7}$$\

and start the discussion about the narrator himself (k = 0 or k = 1)? :P

An answer and a question:
A:

Spoiler

Zoobie got the key: Only the narrator was going to St Ives others were returning from St Ives

Q: Since when did Latex start working with spoilers? They didn't before...

Place 5 pennies so that every penny touches every other penny.

 

[zoobyshoe]

Place 5 pennies so that every penny touches every other penny.

Spoiler

This seems to be impossible, so it may be a trick quetion. The trick solution would be: place a penny. Touch penny 2 to it and set it down. Touch penny 3 to penny 1, then penny 2 and set it down. Continue the pattern for all pennies. The trick being there's no stipulation they all have to touch simultaneously. ?

 

[Jonathan Scott]

Place 5 pennies so that every penny touches every other penny.

Spoiler

I can see that it is possible but it's difficult to describe the solution and even more difficult to actually hold pennies in that shape! Put a penny on the table. Put a pair of pennies side by side on top, touching. On top of that, put a pair arranged in the crossing direction. I then tried tilting them and realized that you can tilt them up, lifting up the middle, until they rest on the bottom penny and touch both of the pennies in the previous layer, which I think is a solution. If there's a simpler solution I can't see it.

P.S. I thought this up in my head but had to get some coins to try it before I was convinced.

 

[Enigman]

There isn't. You got it.

 

[collinsmark]

Here's one that I've used before, but not in this enigma context.

Find the Flaw!

There is a flaw in the following mathematics. Find the flaw, state which line contains the flaw, and specify what the flaw is.

We start with assigning the variable x to a, where a can be constant, or another variable, whatever.

1. \ \ \ \ \ \ x = a
Add x to both sides of the equation.

2. \ \ \ \ \ \ x + x = x + a
Simplify the left hand side of the equation.

3. \ \ \ \ \ \ 2x = x + a
Add "-2a" to both sides of the equation.

4. \ \ \ \ \ \ 2x - 2a = x + a - 2a
Simplify the right hand side of the equation (a - 2a → -a).

5. \ \ \ \ \ \ 2x - 2a = x - a
Factor a '2' from the left hand side of the equation.

6. \ \ \ \ \ \ 2(x - a) = x - a
Divide both sides of the equation by x - a.

7. \ \ \ \ \ \ \frac{2(x - a)}{(x - a)} = \frac{x - a}{(x-a)}
For each side of the equation, cancel out common terms that are in both the numerator and denominator.

8. \ \ \ \ \ \ 2 = 1
Obviously, two is not equal to one. Something dreadful must have happened. Can you spot the flaw and where it is?

Hint: I may accept more than one possible answer, as long as that answer is explained well.

 

[consciousness]

Spoiler

When we assume that x=a, then it follows that (x-a)=0. Hence you can't divide by it.

 

[Enigman]

Collinsmark what have you done?

 

[collinsmark]

Spoiler

When we assume that x=a, then it follows that (x-a)=0. Hence you can't divide by it.

Collinsmark what have you done?

Spoiler

Yes, that's the jist of it. It mostly comes down to step 7. I would have accepted anything like,

• "You're dividing by 0 in step 7 (of course that's obvious now after fumbling around and I subtracted x from a). What the hell are you doing!? You dork!? I hate you!" or alternatively,
• "In step 7, whenever we divide something by another something, we must stipulate that the other something is not zero. So here we must stipulate that the other something, x - a is not zero, meaning x ≠ a. But if we were to introduce the restriction in step 7 of x ≠ a, then that introduces a contradiction with step 1. Therefore step 7 is not possible. yada yada. ... " Well something of that sort anyway.

I work with mathematically inclined people on a daily basis (engineers, myself being one of them). We've all struggled with this one the first time we saw it. But even with love for math, which we might share, maybe, sometimes rigor is thrown to the wind. Enigmas like this make me appreciate the mathematicians' rigor. We in engineering don't have to deal with this stuff that often. But I love the fact that it happens.

 

[Enigman]

Given: A standard narrow-neck coke bottle and a straw
Your mission should you choose to accept it:
1) Drink the coke...yes I know hell's freezing over but no one said its going to be easy...(or you could just throw it away...)
2) Use the straw and without touching the bottle lift the bottle up. Wrapping the straw around the bottle is not allowed.
P.S. @collinsmark- micromass has an interesting blog entry about seeming paradoxes of calculus and how mathematical rigour resolves them, you may want to check them out.

 

[Enigman]

https://www.physicsforums.com/blog.php?b=4566
Found it.

 

[Enigman]

Given: A standard narrow-neck coke bottle and a straw
Your mission should you choose to accept it:
1) Drink the coke...yes I know hell's freezing over but no one said its going to be easy...(or you could just throw it away...)
2) Use the straw and without touching the bottle lift the bottle up. Wrapping the straw around the bottle is not allowed.
P.S. @collinsmark- micromass has an interesting blog entry about seeming paradoxes of calculus and how mathematical rigour resolves them, you may want to check them out.

...

 

[Jonathan Scott]

...

As often happens with these puzzles, the question seems a little unclear.

(a) Do you mean that one must not touch the bottle even with the straw?

(b) How much do you mean by "lift"? Lift it clear of a surface? Or raise it a little?

Spoiler

Or raise it within e.g. a bucket of water?

 

[Enigman]

As often happens with these puzzles, the question seems a little unclear.

(a) Do you mean that one must not touch the bottle even with the straw?

Use the straw as you want, just don't wrap it around the bottle.

(b) How much do you mean by "lift"? Lift it clear of a surface? Or raise it a little?

Mid-air...try over a soft surface if you are looking for a more hands-on approach.