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Puzzle collection
By Sean Farres on Sunday, July 07, 2002 - 01:52 pm:

Hello, try these top puzzles.
A couple I found, some I made.

  1. A 10 digit number, 1st digit tells you how many 1's in the number, 2nd-how many 2's and so on to the last digit telling how many 9's in the number. What's the number?
  2. What are the next 3 lines to this sequence?

    1
    11
    21
    1211
    111221
    312211
    13112221
    1113213211
  3. A man is tied up, he is then tied to a boat (which has no holes in it, before you ask) he is pushed out into a deserted sea drifting along, he can't climb out but after time he drowns. (His boat didn't sink due to heavy rain or splashing water etc. In fact it was a nice hot day!)
    How did he drown?
  4. Which one(s) did I make up(!)?
GOOD LUCK!!!
By Brad Rodgers on Sunday, July 07, 2002 - 07:58 pm:
  1. How can there be a ten digit number with only 9 digits? Do you mean the first digit is the number of 0's? In which case, one answer is

    0123456789
    6210001000

    An interesting question: is this the only solution?
  2. 1 = one 1 ® 11 = two 1's ® 21 ...

    Another interesting question, suppose we represent an as the number of digits in the nth iteration of this. So a1 = 1, a2 = 2 , a3 = 2... Is there ever an n such that an+1 < an? The answer, which I don't yet have, is by no means obvious; if the nth iteration ends up being a string of numbers, say, 11111, then the (n+1)th iteration will consist of less digits (in this case, 2, but sometimes more...). Conway proved that the growth of this function is asymptotic to C.ln, but this doesn't solve my conjecture.
Brad
By Chris Tynan on Sunday, July 07, 2002 - 09:57 pm:

I guess you made up [1] and probably [3], but a friend could have made it up.

for [3], I assume the man is inside the boat?

If so, he could have drowned under his own drool [what a pleasant thought] or he could have used his own body momentum to turn the ship.


Having thought of this - I've been inspired to think up some more problems - all with genuine solutions:

  1. Imagine a court case.

    Two men are accused of murder by a widow.
    However, a anonymous person gives the court a genuine, real video showing one of the men murdering the widow's ex-husband.
    This is enough to make the public believe one of the men is guilty, yet the judge and jury both return a verdict of not guilty for both men.
    Why?

  2. How do you escape from a room with no doors?

  3. From statistical records what is the most dangerous job in America [I've already posted this problem - but no solutions given]

    and finally:
  4. A large group of people from all villages and sectors decide to visit the world's largest and msot accurate atomic clock.
    Whilst many people are amazed by its brilliance and its accuracy, a small group refuse to accept the clock is correct.
    Why?
Good Luck, :)

Chris
By Sean Farres on Monday, August 05, 2002 - 05:05 pm:

Some corrections to the previous set:

Brad was right to say that the first number was how many 0's so forth, plus his answer is correct and the only one I have, though I have been looking in to it more...

A hint to the one about the boat:
Think about the stuff you don't know like for example who the men were or what the boat was made of or what colour the water was...
Some of these are pretty irrelevant!!!

By Sean Farres on Monday, August 05, 2002 - 05:21 pm:

Plus I'll give you 4:

Both number 3 and (of course) 4 are made by me...

They weren't that tough yet - wait until I show my real skills...

By Brad Rodgers on Sunday, July 07, 2002 - 10:08 pm:

For Chris's 3), I think I had a teacher tell me once that teaching was the most dangerous job in America...

By Julian Pulman on Monday, July 08, 2002 - 02:07 pm:

1) The court was trying a murder unrelated to the Widow's ex-husband's murder, so the public believe one of the men is "capable" of murder, but neither man could be found guilty of murdering the man about which the trial intends to determine.

2) The obvious answer is through a window, but I assume by "no doors" you mean "no ways out". I think a true mathematician's answer would be declaring he was already on the outside, and the space bounded outside the walls was "the room".

4) The clock hadn't been started yet?

Julian

By Chris Tynan on Monday, July 08, 2002 - 06:13 pm:

Question 2 is very correct (the second part of your answer) and makes an interesting problem when thought about on a more general scale...

For question [1] I suppose it could be correct, but I should have phrased my question far more clearly, the tape shown is about the murder in question and definitely concludes one of the men guilty of the crime committed, and the case is the case of the murder of the husband.
Still, an inventive solution so well done..

[HINT: Think why two men could both be so closely linked to a murder under the same circumstances]

4] Sorry, the clock is widely accepted as having the correct time - and noone tell me that time is a concept - 'cause I don't want to hear it.

and Brad's teacher is wrong, but not that far off I must say...

By Jo Steer on Tuesday, July 09, 2002 - 01:24 pm:

"In terms of on-the-job safety, physical/mental health, and reputation, it's the most dangerous job in America."
This is probably not the most dangerous job in America from statistical records, but the quote above shows what Michael Ventura at http://www.austinchronicle.com/issues/dispatch/2000-10-13/cols_ventura.html thinks. He is talking about the president.

By Jo Steer on Tuesday, July 09, 2002 - 01:26 pm:

According to the Bureau of Labor Statistics, meat-packing is America's most dangerous job.

By Jo Steer on Tuesday, July 09, 2002 - 01:41 pm:

2) Just to be contrary, a room can have no doors but many doorways. It just means that you don't have to bother to open the door.
1) Maybe the man was acting in self defence? But you say that it shows him "murdering" the husband of the widow, so maybe not. The two men could have been triplets, and the third one who was not found had been the murderer and then disappeared. Or maybe no one could prove which triplet it was, even if it was one of the ones in the court.

By Chris Mycroft on Tuesday, July 09, 2002 - 02:09 pm:

1) they only need be identical twins since as the court could not determine which one it was, both would be aquitted

By Jo Steer on Tuesday, July 09, 2002 - 04:06 pm:

Good point.

By Chris Tynan on Tuesday, July 09, 2002 - 09:34 pm:

Well done Jo and Chris, Jo's answer as president is correct [average of about 11% death rate in office] and Chris's answer is so close and indeed good that it's correct.
I was actually thinking of Siamese twins, thus they could not lock up one man since he would be attached to the other, one of whom is innocent, and locking up an innocent man is forbidden. Bet noone thought of that...

And question 4 still stands unanswered..

By Arun Iyer on Tuesday, July 09, 2002 - 09:50 pm:

For your 4,
it seems illiteracy is the answer...out of the large group of people,a small group is illiterate and as we know illiterate mind refuses to accept anything new...

love arun

By Chris Tynan on Tuesday, July 09, 2002 - 09:55 pm:

While your answer appears correct Arun, the illiterate group must have had a time in the first place, which obviously matches the time given on the clock [give or take time difference].

The answer is something more complex, and if noone guesses I'll post it tomorrow...

At least a few people replied this time, I may have to think up or get some new puzzles.

Chris

By Saul Foresta on Wednesday, July 10, 2002 - 12:17 am:

One question for number four chris, is the small group justified in not trusting the clock's accuracy?

By Chris Tynan on Wednesday, July 10, 2002 - 06:18 pm:

Yes. Definitely

By Yatir Halevi on Sunday, July 14, 2002 - 02:59 pm:

Chris,
The way to escape from the room is to die...hmm...

Yatir

By Jo Steer on Monday, July 15, 2002 - 01:08 pm:

4) Maybe the people who doubt its accuracy are very precise people and consider the one nanosecond out every trillion years makes the clock very inaccurate. But I don't think that's the answer. You said that you would post the answer if no one had guessed it by July 10th. Please!

By Chris Tynan on Monday, July 15, 2002 - 06:34 pm:

OK - I left it for a few days just to see if anyone could guess.

The rather peculiar answer is that the people are members of a minor religous group. The founders of this group run several days behind everyone else in terms of time, because when everyone changed to the Gregorian calendar a long time ago, they did not, so they have a different calendar.
Admittedly, this was a very hard problem.

By Julian Pulman on Friday, July 19, 2002 - 12:47 am:

Not meaning to sound like a "sore loser", but you have to admit that most of these answers given are plausible..it's a bit like the following question:

Q) What is the next term in the following series?

0,1,2,3,4,

Of course, the majority of people would reply their answer as "5", ie an = n.
But, actually, the answer is 0, I was using the formula an = n (mod 5). Similarly, the sequence could represent the ages of the first few people I could think of, 5 younger siblings and then my grandad aged 73 (0,1,2,3,4,73).

Getting more philosophical, to what extent does it matter that we get the right answer, from the wrong formula? What if my generating formula was actually an = n (mod n+1)? or how about an being the nth digit of 10/81? (n<8)
Curiously, the Schwartzchild Radius of a Black Hole was derived incorrectly in 1793, but yielding the correct formula...
Could such anomalies actually stunt development? If our formula satisfies observation (because it is true) why should we have reason to doubt our method of derivation when in fact it is entirely flawed? Sometimes, as history as shown, the correct derivation reveals that our formula is actually an implication of a far stronger, and more critical result - an example, the General Theory of Relativity which shows how space and time are actually not independant and that mysterious force called gravity which strangely brings objects together is only reminisent of the fact that mass/energy deforms spacetime - Newton's Law of Gravitation can be derived simply from these concepts.

Sorry to add this unrelated touch to the thread, so to return, I'll add to the riddles:

Poor Man has it
Rich Man wants it
It is stronger than God
It is more evil than Satan
And if you eat it, you will surely die

What is it?


Julian

By Saul Foresta on Friday, July 19, 2002 - 02:04 pm:

In response to Julian, it is nothing.