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
  • #771
zoobyshoe said:
Good one!

Heh, that reminds me of this old one:

hippomonstrosesquippedaliophobia - with how many letters is it spelled?
 
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  • #772
billiards said:
• take label off "apples and oranges box"
• take fruit out of "apples and oranges" box.
• if apple: take label off "apples" box and put on the old "apples and oranges" box.
• take label off the "oranges" box and put on the old "apples" box.
• put the "apples and oranges" label on the old "oranges" box.

if you pick an orange then ammend above instructions by interchanging the word "apples" for "oranges" and vice-versa.
Tadashii!
(Correct in japanese)
CompuChip said:
Heh, that reminds me of this old one:

hippomonstrosesquippedaliophobia - with how many letters is it spelled?
Two.


Enigman said:
Another one:
a-question-of-time.jpg

The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?
---------------
Previous one was too easy. And Sam Loyd was one of the greatest puzzle makers in history...

(Reposted so that no one misses it)
 
  • #773
Hint:
Given: time= 8hrs + x min
angle between hands is bisected by 6 hour mark.
1 min--> 1/60 deg of hours hand
 
  • #774
Enigman said:
Hint:
Given: time= 8hrs + x min
angle between hands is bisected by 6 hour mark.
1 min--> 1/60 deg of hours hand

Isn't this just trivial algebra? 30 - x = 10 + (x/12) so x = (12*(30-10))/(12+1) = 18 + 6/13
 
  • #775
Jonathan Scott said:
30 - x = 10 + (x/12) so x = (12*(30-10))/(12+1) = 18 + 6/13

Correct though incomplete:
extending the solution: 8hrs 18 min 27 + 9/13 sec.
LaTeX doesn't work in spoilers :frown:
 
  • #776
An odd bit of history:

Arthur O'Connor of the Society of United Irishmen wanted to petition the French to support an Irish revolution, on his way to France he was arrested and imprisoned in Fort George but on his way to the prison he distributed the following verse:

"The pomps of Courts and pride of kings
I prize above all earthly things;
I love my country, but the king,
Above all men, his praise I sing.
The Royal banners are displayed,
And may success the standard aid.
I fain would banish far from hence.
The 'Rights of Man' and 'Common Sense'
Confusion to his odious reign,
That foe to princes, Thomas Paine.
Defeat and ruin seize the cause.
Of France, its liberties and laws."

-On the first glance it seems he had a change of heart and had become suddenly loyal to the throne but of course, that's not even near the truth...
So what's the true meaning of the verse?
I believe I already gave a hint...did you notice?

Oh and don't google the guy if you don't want to cheat... google him after you get the Enigma and the cat's safely outside the box (or dead).
 
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  • #777
I wonder if the verses were written side-by-side?
 
  • #778
Jonathan Scott said:
I wonder if the verses were written side-by-side?

No they weren't...but do go on...box seems to be opening...
Edit-
it seems I oversimplified it a bit by making two different stanzas...edited that...
I will accept your answer as that works too...
Odd-
(1) The pomp of courts, and pride of kings,
(3) I prize above all earthly things;
(5) I love my country, but my king,
(7) Above all men his praise I'll sing.
(9) The royal banners are display'd,
(11) And may success the standard aid:
Even-
(2) I fain would banish far from hence
(4) The Rights of Man and Common Sense.
(6) Destruction to that odious name,
(8) The plague of princes, Thomas Paine,
(10) Defeat and ruin seize the cause
(12) Of France, her liberty, and laws.
 
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  • #779
Find the smallest palindromic number which is a perfect square and has an even number of digits.
 
  • #780
Another one I can't believe I haven't asked yet...
Its a fruity one too!
(though I don't know if Gad's still following the thread...)
In a closed circular room there are 31 people standing such that everyone can see everyone else. Your job is to place a pomegranate such that all except one can see the fruit.
 
  • #781
Enigman said:
Another one I can't believe I haven't asked yet...
Its a fruity one too!
(though I don't know if Gad's still following the thread...)
In a closed circular room there are 31 people standing such that everyone can see everyone else. Your job is to place a pomegranate such that all except one can see the fruit.

I'll have a go...

One wall is a mirror. 30 people face the mirror, 1 person faces them with his back to the mirror. Place the pomegranate behind this person.
 
  • #782
No mirrors and no smoke...
as its a silly one I will give it to you anyway.
:smile:
my answer was:
place it on the person's head...:-p
Now the more serious one:
Find the smallest palindromic number which is a perfect square and has an even number of digits.
EDIT: not writing a computer program would be appreciated...
 
  • #783
Enigman said:
EDIT: not writing a computer program would be appreciated...
Darn it.
 
  • #784
Enigman said:
Find the smallest palindromic number which is a perfect square and has an even number of digits.
Does it have to be palindromic in base ten?

[STRIKE]If not, then I'd say nine (binary: 1001), which is a perfect square of three (32 = 9, or if you prefer in binary, 11 × 11 = 1001), and has an even number of bits (does the term "digit" imply base ten? Hmm).[/STRIKE] Edit: Nevermind, see next post.
 
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  • #785
Enigman said:
Find the smallest palindromic number which is a perfect square and has an even number of digits.
My new guess is four (ternary 11). It is a perfect square of two, (ternary, 2 × 2 = 11), it is palindromic in base 3, and has an even number of digits in base 3.
 
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  • #786
Just base ten collinsmark...
(For a smallest number it doesn't seem really small enough...
6 digits
)
 
  • #787
collinsmark said:
Darn it.

Btw collinsmark I did solved it with C++... the clause was just so that I could see if someone's able to solve without programming...I couldn't.
:blushing:
 
  • #788
Enigman said:
Btw collinsmark I did solved it with C++... the clause was just so that I could see if someone's able to solve without programming...I couldn't.
:blushing:

Nor could I in base 10. Well, not without incrementally checking numbers manually. Computers are better at stuff like that.

Code:
using System;

// This is a C# program that finds the
// smallest perfect square that
// is palindromic in base 10,
// and has an even number of
// digits in base 10.
namespace Enigman_Palindrome_thing
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = 2; // This is the root of the perfect square.
            
            // Now let's loop through the natural numbers to find
            // the palindromic, even digited, perfect square.
            bool foundIt = false;
            while(!foundIt)
            {
                int nSquared = n * n; // this is the number to check.
                string nSquaredString = nSquared.ToString(); // string form.

                // Let the console know which number we're checking.
                Console.WriteLine("Currently checking " + nSquaredString);

                // check if it has even number of digits. 
                if((nSquaredString.Length)%2 == 0)
                {
                    // If we're here it's even. Check if it's a palindrome.
                    bool palindromeFlag = true;
                    for(int i = 0; i<nSquaredString.Length/2; i++)
                    {
                        // If symetric characters are not equal, 
                        // then it's not a palindrome.
                        if (!(nSquaredString[i] 
                            == nSquaredString[nSquaredString.Length - 1 - i]))
                            palindromeFlag = false;
                    }
                    if(palindromeFlag)
                    {
                        // Found it! let's report it to screen
                        // and finish up. 
                        foundIt = true;
                        Console.WriteLine(Environment.NewLine
                            + "Found it! The number is "
                            + nSquaredString + " which is "
                            + n.ToString() + " squared.");
                    }
                }
                // Increment n for next number to check.
                n++;
            }
            // Keep console alive until ready to leave.
            Console.ReadKey();

            // Goodbye!
        }
    }
}
 
  • #789
Okay, you probably missed giving the final answer amidst copying your code so:
836^2=698698
 
  • #790
There are eight oranges in a box. How can you divide them between eight people so that each person gets one orange, and one orange is still left in the box?
The oranges must not be peeled or cut.
 
  • #791
Enigman said:
Okay, you probably missed giving the final answer amidst copying your code so:
836^2=698698

Or more correctly ...
836^2=698896

I see (from a one-line REXX program) that the next one has 12 digits, but I didn't have the patience to find the third one!
 
  • #792
Enigman said:
There are eight oranges in a box. How can you divide them between eight people so that each person gets one orange, and one orange is still left in the box?
The oranges must not be peeled or cut.

Is it OK if one person gets a box as well, then?

(Edited to use spoiler tags - I thought I was just asking for clarification of the question!).
 
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  • #793
Jonathan Scott said:
Is it OK if one person gets a box as well, then?

Done!
Oh, and spoiler it. :wink:
 
  • #794
What is the maximum number of kings that can be placed on a chess board so that none of them threatens any other?
EDIT: A better way to put it would be maximum number of independent kings...
 
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  • #795
Is that so that they all can't move as moving each King would place itself into check, or that they are positioned in a way that there is a concievable pattern of movements such that all kings could make movements which would ultimately lead to a draw?
 
  • #796
Travis_King said:
Is that so that they all can't move as moving each King would place itself into check, or that they are positioned in a way that there is a concievable pattern of movements such that all kings could make movements which would ultimately lead to a draw?

The only condition is that the largest number of (independent ie. each of a different player or colour) kings should be on board without any king being in 'check' in the arrangement. So, the former follows from the conditions.
See- https://www.physicsforums.com/showpost.php?p=4575363&postcount=754 (same thing with knights)
This one too is a variation of the 8 queen puzzle. (Find an orientation such that there are 8 queens on board without being threatened ('checked') by any other)

A more mathematical restatement would be- in 8x8 square place maximum number of pieces so that there is always more than (or equal to) 1 unit^2 space between two pieces. or something like that...
 
  • #797
Enigman said:
What is the maximum number of kings that can be placed on a chess board so that none of them threatens any other?
EDIT: A better way to put it would be maximum number of independent kings...
By trial and error only:
16?
 
  • #798
Last edited:
  • #799
(I deleted the previous one posted here on grounds of being too silly)
If it takes four men eight days to dig four holes, how long does it
take one man to dig half a hole?
 
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  • #800
Enigman said:
(I deleted the previous one posted here on grounds of being too silly)
If it takes four men eight days to dig four holes, how long does it
take one man to dig half a hole?

I find the concept of "half a hole" rather difficult.

Is this meant to be a trivial maths question where the holes are assumed to require a fixed amount of work and "half a hole" means half the amount of work?
 
  • #801
The problem statement is all you get.
:biggrin:
(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)
 
  • #802
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!
 
  • #803
Travis_King said:
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!
 
  • #804
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?
 
  • #805
Do we also assume they each run just as far as in the first race? :P
 

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