Solve Enjoyable Enigmas with Mr.E's Challenge

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OK - another dead body, adapted from one of Captain W.E. Johns' Biggles short stories set in the late '40s or early '50s.

A fourteen year old girl leaves school alone on foot at her usual time. She is later found dead, on her usual route home, killed by a single blow to the head. The only habitation close by is a manor house. No one there saw or heard anything suspicious. The only thing out of place at the crime scene is an expensive box of chocolates on the ground nearby. The police are stumped.

At the invitation of Inspector [strike]Lestrade[/strike]Gaskin, Biggles goes to have a look around. While they are at the crime scene, he notices the 20-ish daughter of the family who own the manor house walking up and down the garden holding hands with a man in RAF uniform. Gaskin comments that it was the daughter's birthday the day of the murder, and Biggles immediately suggests arresting the man in uniform. Why?
 
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Ibix said:
OK - another dead body, adapted from one of Captain W.E. Johns' Biggles short stories set in the late '40s or early '50s.

A fourteen year old girl leaves school alone on foot at her usual time. She is later found dead, on her usual route home, killed by a single blow to the head. The only habitation close by is a manor house. No one there saw or heard anything suspicious. The only thing out of place at the crime scene is an expensive box of chocolates on the ground nearby. The police are stumped.

At the invitation of Inspector [strike]Lestrade[/strike]Gaskin, Biggles goes to have a look around. While they are at the crime scene, he notices the 20-ish daughter of the family who own the manor house walking up and down the garden holding hands with a man in RAF uniform. Gaskin comments that it was the daughter's birthday the day of the murder, and Biggles immediately suggests arresting the man in uniform. Why?

I had a dream last night that I solved this. Gwahhh! Why can't I remember the specifics of my dream. :cry:

(There's a good chance the solution involves zombies.)
 
Ibix said:
OK - another dead body, adapted from one of Captain W.E. Johns' Biggles short stories set in the late '40s or early '50s.

A fourteen year old girl leaves school alone on foot at her usual time. She is later found dead, on her usual route home, killed by a single blow to the head. The only habitation close by is a manor house. No one there saw or heard anything suspicious. The only thing out of place at the crime scene is an expensive box of chocolates on the ground nearby. The police are stumped.

At the invitation of Inspector [strike]Lestrade[/strike]Gaskin, Biggles goes to have a look around. While they are at the crime scene, he notices the 20-ish daughter of the family who own the manor house walking up and down the garden holding hands with a man in RAF uniform. Gaskin comments that it was the daughter's birthday the day of the murder, and Biggles immediately suggests arresting the man in uniform. Why?

Not sure if I've got the hang of these but my guess:

pilot dropped chocolates out of plane on way to his girlfriend's birthday party, hit poor girl on the noggin
 
Okay thread's lagging...time for a reboot:
So... Chess:
Anand currently is getting his a** kicked1 and Kasparov's probably grinning ear to ear...
but that has nothing to do with this Enigma.

What is the maximum number of knights that can be arranged on a standard chess board such that not one of them threatens any other or is threatened by any other? ie. no one faces a check.
-----------------------------------------------------------------------------------------
1 (as of now, if at the time you are reading this it doesn't hold true...I'm a happy man)
 
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Enigman said:
Okay thread's lagging...time for a reboot:
So... Chess:
Anand currently is getting his a** kicked1 and Kasparov's probably grinning ear to ear...
but that has nothing to do with this Enigma.

What is the maximum number of knights that can be arranged on a standard chess board such that not one of them threatens any other or is threatened by any other? ie. no one faces a check.
-----------------------------------------------------------------------------------------
1 (as of now, if at the time you are reading this it doesn't hold true...I'm a happy man)

32. All the dark squares (or all light squares)
 
billiards said:
32. All the dark squares (or all light squares)

Correct. This one was a different take on the 8 queens puzzle, place 8 queens such that none of them threaten any other, there are more than one solutions. (and if you can do it then try doing it under 43 secs which is my best record...
:superiour irritating smirk:*)

Next one:
Find a number such that it is three times the sum of its digits.
-----------------------
*I need more emoticons :frown:
 
Enigman said:
Correct. This one was a different take on the 8 queens puzzle, place 8 queens such that none of them threaten any other, there are more than one solutions. (and if you can do it then try doing it under 43 secs which is my best record...
:superiour irritating smirk:*)

Next one:
Find a number such that it is three times the sum of its digits.
-----------------------
*I need more emoticons :frown:

27

I'll stop getting them now. :blushing:
 
Consider the numbers 43 and 34. We can say one is the reverse of the other.

Consider an isosceles triangle. The two base angles are the same.

It was determined here at PF that there exists a finite number of isosceles triangles whose base angles are the reverse of their apex angle. The total number of these is <10.

Find them and give the angles.
 
Let triangle be ABC
base angle (<ABC and <ACB)=(100a+10b+c)
<ABC+<ACB >180 if a>1
:.a=0
Base angle=10b+c
20b+2c+10c+b=180
21b+12c=180
7b+4c=60
b has to be even
4,8
8,1
48,84
81,18
 
Enigman said:
Let triangle be ABC
base angle (<ABC and <ACB)=(100a+10b+c)
<ABC+<ACB >180 if a>1
:.a=0
Base angle=10b+c
20b+2c+10c+b=180
21b+12c=180
7b+4c=60
b has to be even
4,8
8,1
48,84
81,18

Correct!
 
Here's a good one. Originally this riddle was phrased such that yes or no questions were pretty much essential. I've tried to rephrase it here, putting as much information I can directly into the riddle's wording. I'll still entertain any yes or no questions, but it might not do any good. The essentials are in the riddle. [Edit: well, except perhaps for that Eureka moment.]

Angus, age 34, is found guilty of heinous, heinous crimes by a full jury -- crimes so heinous that describing them in detail might violate the forum rules. Suffice it to say that the crimes involved murdering many people, including most of his own family (plus he did even more heinous stuff, besides just the murders).

Upon sentencing, the judge says to Angus, "You have been found guilty by a jury of your own peers. I would like to sentence you to life in prison many, many times over, if only I could. Unfortunately that option is not available in this case. You are released without prison time, and without punishment. You may leave the courtroom in the custody of your only surviving relative: your brother Malcolm, who is an upstanding, law-abiding citizen."

Why did the judge not sentence Angus to prison?​

Here's a few clarifications that might help.
  • Diplomatic immunity has nothing to do with this riddle.
  • The situation happens in a first world country that prides itself on its fair judicial system (the specific country is not relevant). The country (and its legal system) is not corrupt, respects victims' rights and the rights of the innocent, does not torture, does not falsely imprison, does not engage in cruel and unusual punishment, etcetera, etcetera.
  • There's nothing broken in the prison system. It's not completely filled with prisoners or anything like that. There are other people still going to prison for other crimes.
  • Nobody in the courtroom (including Angus and Malcolm) is facing a terminal illness.
  • Angus is not in political office, or in a position of political power.
 
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Would Angus be a conjoined twin, fused to his brother, Malcom?
 
collinsmark said:
Correct! :smile: (Golly, I didn't think someone would get the answer so quickly.)
Mysteries at the Museum has a segment on these guys:

http://en.wikipedia.org/wiki/Chang_and_Eng_Bunker

that I've seen a few times. Once I concentrated on determining the reason imprisonment wasn't an option in this case, this situation soon occurred to me.
 
Next one:
Rearrange the following letters to make one word:
NEW DOOR
 
Enigman said:
Next one:
Rearrange the following letters to make one word:
NEW DOOR

one word
:biggrin:
 
billiards said:
one word
:biggrin:
Good one!
 
Next one:
There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges".

But the labeling machine has gone crazy and is now labeling all boxes incorrectly.

If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?
 
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...
 
Enigman said:
Next one:
There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges".

But the labeling machine has gone crazy and is now labeling all boxes incorrectly.

If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?

• 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.
 
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)
 
Hint:
Given: time= 8hrs + x min
angle between hands is bisected by 6 hour mark.
1 min--> 1/60 deg of hours hand
 
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
 
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:
 
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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I wonder if the verses were written side-by-side?
 
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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Find the smallest palindromic number which is a perfect square and has an even number of digits.
 
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.
 

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