Solve Enjoyable Enigmas with Mr.E's Challenge

  • Thread starter Enigman
  • Start date
In summary: Four princes approach the king vying for the hand of the princess. In order to choose the best among the four suitors the king and the princess arrange a test: the suitors are brought to a large rectangular hall. The floor is covered with a carpet all over except at the corners- where there are four squares of bare floor and the suitors are told to stand at these corner. Each suitor takes a corner and stands there while the princess stands at the center of the hall. The king then proclaims the prince who without leaving their respective squares shall put a ring on the princess's hand will be declared to be the bridegroom of his daughter and the heir to Enigmania. No ropes or rods are
  • #246
Enigman said:
Yes, that was my answer too; but the dragon wouldn't bring #6- he would bring #7 as there is no antidote for #7...just nitpicking.
I know. I had this weird idea that, even though he was a dragon, it would be less trouble for him to bring #6, and it wouldn't make any difference since the knight couldn't get to #7.
EDIT: On a bit of further thought the knight will probably be safer drinking from #1.
Yes, that would be the safest.
 
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  • #247
Enigman said:
Now, that was delicious.
Knight drank the water from a well numbered between 1-6 before coming to the duel and brought pure water to the duel while dragon brought water from 7. After the exchange of glasses Knight was cured by dragon's water while the dragon thinking that water was poisoned went and drank from 7 to cure it and hence died.
Am I Correct?

Yes this is the cleanest solution.
There is no controversy about the availability of
non lethal water because they were on an island! Quite elegant.
 
  • #248
In the distant land of Enigmania, where the King Enigmaniac ruled there was a large gold mine. In the gold mine worked a thousand dwarves who mined gold and smelted the gold into gold bars. Each dwarf produced a thousand gold bars of 1000 grams each day. One day a guard came from the mines and told the king that he had overheard a dwarf talking to himself how he was making bars of only 999 grams and taking 1 gram from each bar for himself. By the time the guard reached the place where the echoes were coming from the dwarf had fled hearing the guard's footsteps. Enigmaniac wanted to apprehend the dwarf but had no way of doing so as then the scales were very inaccurate. Enigmaniac then called upon his Grand Wizard EnigmaX. EnigmaX summoned a hi-tech digital scale but said that the scale would remain for only one measurement- as soon as the button to show the weight of load is pressed the scale will show the result and disappear. So what should be done to apprehend the dwarf?
(Assume that only one dwarf is cheating and all others make bars of exactly 1000 grams. Sorry about the wall of text, didn't remember the exact wording of the riddle- shouldn't make much difference though as its purely a mathematical one.)
 
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  • #249
You're saying they only have one shot ever and forever at getting an accurate weight? They cannot re-summon the scale as needed?
 
  • #250
Yep. EnigmaX's spell has got some serious limitations but nothing a bit of logic* can't overcome.

*which I didn't have apparently as I failed this one...
 
  • #251
Enigman said:
Yep. EnigmaX's spell has got some serious limitations but nothing a bit of logic* can't overcome.

*which I didn't have apparently as I failed this one...
I'm not sure how yet, but assuming they can use one weigh-in to locate the underweight bars, they have some way of connecting those bars to the dwarf who cast them?
 
  • #252
The dwarves will bring only the gold bars they themselves have cast when the weighing is done. So, yes.
EDIT: but that won't help much, if more than one dwarf's gold is brought you can't tell the bars apart.
 
  • #253
Huge Hint: think in terms of number sequences and their sums...
 
  • #254
Enigman said:
Huge Hint: think in terms of number sequences and their sums...
I think this is it (the clue was vital) :

Arbitrarily give each dwarf a number from 1-1000 and record which dwarf got which number. Then make each dwarf put a number of gold bars on the scale equal to the arbitrary number that has been assigned him. In this way you create an arithmetical sequence that can be summed. Calculate the sum and then calculate what the sum should weigh. Then weigh all the bars in the series.

The actual weight will be something less than the expected weight because some number of bars weighing only 999grams will have been included. By subtracting the actual weight from the expected weight (all in grams), you will get a difference that is some whole number. That is the arbitrary number that has been assigned to the dwarf who has been making the underweight bars. E.g., the sum of the sequence 1-1000 is 500,500. At 1000 grams each, this many bars should weigh 500,500,000 grams. If the actual weight is 500,499,258, then it is 742 grams underweight. Dwarf #742 must have put 742 bars weighing only 999grams each on the scale.
 
  • #255
Yes indeed that is correct.
 
  • #256
Enigman said:
Yes indeed that is correct.
Happy to hear that! That one was hard! Took me hours to sort it out.
 
  • #257
The real question is how did the dwarf know he was only smelting 999 grams each time if the king couldn't tell with his own scale technology?

OK here's a riddle. One hundred people are to be lined up tomorrow, all of them facing the front of the line (so they are looking directly at someone's back, except for the person in front). On each of them will be placed a black hat or a white hat. In any order they each can call out either "black" or "white" once, and only once, and make no other noise. If at least 99 of them call out the correct color of the hat on their head, everyone wins one hundred dollars.

Describe how they can guarantee a victory.

EDIT: Corrected for missing details
 
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  • #258
Office_Shredder said:
The real question is how did the dwarf know he was only smelting 999 grams each time if the king couldn't tell with his own scale technology?

OK here's a riddle. One hundred people are to be lined up tomorrow, all of them facing the front of the line (so they are looking directly at someone's back, except for the person in front). On each of them will be placed a black hat or a white hat. In any order they each can call out either "black" or "white" once, and only once. If at least 99 of them call out the correct color, everyone wins one hundred dollars.

Describe how they can guarantee a victory.

The person standing last will call out the colour of the hat of the person who is standing in front of him. The 99th person will thus know his colour. Now 99 people will follow the following rules-
1)If their colour is same as that of the person standing in front of them they will call out their colour immediately.
2)If their colour is different they will wait.
By doing this the nth person will know their colour provided that the (n+1)th person knows their coulour. By a "reverse mathematical induction" All the 99 people left will know their colours. This will reqiure a lot of coordination on the part of the 99 people though.
 
  • #259
Office_Shredder said:
The real question is how did the dwarf know he was only smelting 999 grams each time if the king couldn't tell with his own scale technology?

OK here's a riddle. One hundred people are to be lined up tomorrow, all of them facing the front of the line (so they are looking directly at someone's back, except for the person in front). On each of them will be placed a black hat or a white hat. In any order they each can call out either "black" or "white" once, and only once. If at least 99 of them call out the correct color, everyone wins one hundred dollars.

Describe how they can guarantee a victory.
A "correct" color means?
 
  • #260
zoobyshoe said:
A "correct" color means?

The colour of the hat on their head I assume.
 
  • #261
Yes, correct means they call out the color of the hat on their head, sorry.

consciousness, that looks correct but as an added challenge
it's possible for them to solve the problem without needing to time the statement of their answers (i.e. there is a deterministic algorithm for who goes next that everybody can run, and not wonder if the person behind them has finished waiting to state their color or not - a problem which could occur if five or six people in a row are supposed to wait). Alternatively you could just have them state their color in weird accents to transmit the additional information :p
 
  • #262
Office_Shredder said:
The real question is how did the dwarf know he was only smelting 999 grams each time if the king couldn't tell with his own scale technology?

OK here's a riddle. One hundred people are to be lined up tomorrow, all of them facing the front of the line (so they are looking directly at someone's back, except for the person in front). On each of them will be placed a black hat or a white hat. In any order they each can call out either "black" or "white" once, and only once. If at least 99 of them call out the correct color, everyone wins one hundred dollars.

Describe how they can guarantee a victory.
They work out a code whereby each tells the one in front of him what color hat he's wearing. The code might be anything. Let's say it's clearing the throat before calling out, vs no throat clearing. A throat clearing means, "Your hat is the opposite color of the one I'll call out." No throat clearing means, "Your hat is the same color as the one I'll call out." They could use clearing the throat, or not clearing it, coughing or not coughing, whatever audible vocal tick they all agree to.. They start at the back of the line and work forward in order. The guy at the very back simply calls out the color of the guy in front of him. Even if that's not his own hat color, 99% will still be right. Each will correctly call out the color of his own hat and simultaneously tip the person in front of him off to their correct hat color.
 
  • #263
I edited the original question to prevent wiseassery :-p
 
  • #264
Office_Shredder said:
Yes, correct means they call out the color of the hat on their head, sorry.

consciousness, that looks correct but as an added challenge
it's possible for them to solve the problem without needing to time the statement of their answers (i.e. there is a deterministic algorithm for who goes next that everybody can run, and not wonder if the person behind them has finished waiting to state their color or not - a problem which could occur if five or six people in a row are supposed to wait). Alternatively you could just have them state their color in weird accents to transmit the additional information :p

Okay I have another solution that solves the 5-6 persons waiting problem.
The 100th person calls out the colour of the 99th person. Now the 99th person compares the colour of the 98th person with the 1st person (who presumably everyone can see).
1)If the colours are same he calls out his own colour. The 98th person now knows his colour and plays the role of the 99th person from next loop.
2)If the colours are not same he doesn't say anything. Then the 98th person immediately calls out his own colour.
Cycle is repeated till there are only two persons left, the first who doesn't know his colour and another who does. By an agreement if the other person doesn't call then the colour of the first is opposite to that of the other person. If he calls then the colours are same.
Probably my last solution because my ideas keep on getting more and more convoluted. :biggrin: Pretty soon my solution will be longer than the proof of Fermats last theorem. :smile:
 
  • #265
Office_Shredder said:
I edited the original question to prevent wiseassery :-p
What wiseassery?
 
  • #266
Office_Shredder said:
I edited the original question to prevent wiseassery :-p

You are forgetting that 'wiseassery' is often the point of this thread. Anything goes- within the limits of the question. Most of the answers depend on how the question was worded; what was said and what was omitted- which makes framing the question correctly quite a pain in the back.

Next one:
You are at your home sitting on the sofa reading a book. Suddenly a snow ball crashes through the window, you look out of the broken* window to see the three brothers from next door -John , Mark and Fred run around the corner and me standing there enjoying the show :devil:
You ask me who did it. I write the following thing to you on a scrap of paper "?, he broke your window."
So who would you question/scold/have your yard work done by for free?
(Except me, I am off limits. Oh, and I didn't break your window and am telling the truth- enigmatically though it may be...)
EDIT:*broken.
 
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  • #267
Office_Shredder said:
OK here's a riddle. One hundred people are to be lined up tomorrow, all of them facing the front of the line (so they are looking directly at someone's back, except for the person in front). On each of them will be placed a black hat or a white hat. In any order they each can call out either "black" or "white" once, and only once, and make no other noise. If at least 99 of them call out the correct color of the hat on their head, everyone wins one hundred dollars.

Describe how they can guarantee a victory.

EDIT: Corrected for missing details
If the person in front of you has a white hat, place your hand on their left shoulder. Otherwise place your hand on their right. Then it doesn't matter what order they get called to reveal their hat color.
 
  • #268
Enigman said:
You are forgetting that 'wiseassery' is often the point of this thread. Anything goes- within the limits of the question. Most of the answers depend on how the question was worded; what was said and what was omitted- which makes framing the question correctly quite a pain in the back.

Next one:
You are at your home sitting on the sofa reading a book. Suddenly a snow ball crashes through the window, you look out of the window to see the three brothers from next door -John , Mark and Fred run around the corner and me standing there enjoying the show :devil:
You ask me who did it. I write the following thing to you on a scrap of paper "?, he broke your window."
So who would you question/scold/have your yard work done by for free?
(Except me, I am off limits. Oh, and I didn't break your window and am telling the truth- enigmatically though it may be...)

A snow ball?.. I'd say the window was open.

Unless the snow ball hides a small rock in it, that'll be a different scenario. :devil: Oh I miss those days. :biggrin:
 
  • #269
Gad said:
A snow ball?.. I'd say the window was open.

Nope, your window definitely broke.
Unless the snow ball hides a small rock in it, that'll be a different scenario. :devil: Oh I miss those days. :biggrin:
Me too...:cry:
 
  • #270
Enigman said:
Nope, your window definitely broke.

It was broken before? :biggrin:
 
  • #271
Snowball broke the window. You are :mad:.
Who broke it? -I already answered that o:).
 
  • #272
Well, move on to the next Enigmas, I'll do the yard work. :biggrin:
 
  • #273
Solve this one first...
Saying what I wrote aloud may help
AV2.gif
 
  • #274
Enigman said:
Next one:
You are at your home sitting on the sofa reading a book. Suddenly a snow ball crashes through the window, you look out of the broken* window to see the three brothers from next door -John , Mark and Fred run around the corner and me standing there enjoying the show :devil:
You ask me who did it. I write the following thing to you on a scrap of paper "?, he broke your window."
So who would you question/scold/have your yard work done by for free?
(Except me, I am off limits. Oh, and I didn't break your window and am telling the truth- enigmatically though it may be...)
EDIT:*broken.
"?, he broke your window" = "Question Mark, he broke your window."
 
  • #275
Yep, ZBS that is correct.
 
  • #276
Borg said:
If the person in front of you has a white hat, place your hand on their left shoulder. Otherwise place your hand on their right. Then it doesn't matter what order they get called to reveal their hat color.
Comment and variation of your solution:
They're not called on to give their hat color. They decide when to speak up. Regardless, I think your solution should be counted as correct. I'm afraid Office Shredder will condemn it as "wiseassery," though.

Anyway, your thinking outside the box gave me an idea for another, similar, solution. Hitherto, I've been stuck thinking the last person has to be the sacrificial one who does not call out his hat color with 100% certainty. We could make the first person the sacrificial one, though, by exploiting even more non-prohibited options.

After the line is formed and all the hats are in place, everyone could take a second to check out the hat color of the person in front of them, then they could reach forward, grab the hat off that person's head, and put it on their own head. The first person would be left hatless, and there'd be an extraneous hat at the end of the line, but 99 of them would all now know the color of the hat on their head with 100% certainty. They could call out from front to back or visa versa, depending on which they decided.

I get the sense Office Shredder has some much more mathematical solution in mind. I've been thinking all day and nothing like that has occurred to me.
 
  • #278
Another one that I love-

You die and the devil says he'll let you go to heaven if you beat him in a game. The devil shows you a round table (perfectly circular). He gives himself and you a huge pile of quarters. He says "ok, we'll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. We can put the quarters anywhere on the table.The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart, and you know that if you go first, you can guarantee victory. Explain how you can guarantee victory.

Take your time on this one, easy to understand but challenging to solve :devil:.
 
  • #279
I think I got it but I don't have the mathamatical proof for it and am just going on intuition...
The first goes into the center (as that is the only unique position) then the rest go diametrically opposite to the 2nd player's ie. devil this will ensure(I think) that all the possible places are already taken up when the final turn of devil comes
I will need some time to come up with the proof (that is of course if I can and if the answer is correct...)
BTW- I am prepared to meet the devil, but whether he is prepared to meet me is an entirely different matter.*
}:-D
*Paraphrasing Churchill
 
  • #280
Only an odd number of quarters complete the circle, the odd one being at the center. But I'm too lazy to do the math. :p

On a side note, I don't know why stoichiometry jumped to mind? *shakes head*
 

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