Brain Teaser No 1

This one is doing my head in. I'm certain that it's all about solving simultaneous equations, if only I could work out which ones! More cold towels for the head please nurse ...

THE ANSWER IS 75 MILES.

I WON'T STEAL YOUR THUNDER (OR SPOIL IT FOR OTHERS)BY GIVING THE EXPLANATION.
A CLASSIC SAM LLOYD PROBLEM THOUGH!

STEVE D

The following brain teasers still need a bit of work to sort out.

Bam's gold lame gameshow - does it matter whether Paul S doesn't know where the NAP500 is and opened the doors at random or knows where the NAP500 is and deliberately opened 'empty' doors until he got to the last one. Perhaps we should try thinking of (say) 10 doors rather than 3 or a million!!!

Identifying the odd ball. We know the answer is 3 and Duncan F (and no doubt others - but not me) have found the solution on other web sites and are gallantly holding off giving the answer until the rest have sweated a short while!

Confirming that it is 75 miles to Salisbury (or is it?) using simultaneous equations that take us back to school (except for SteveD who is also galantly holding of)and give Duncan headaches and a desire for nurses.

So no more music until the work is done

Anybody got any more, before I post my last couple?

Cheers

Don

[edited]
Well, looks like I cannot upload a Word file or html. and I'm not artistic enough to draw the equations using MS Paint.

The "500 Giveaway" teaser all became clear to me in a flash of insight the other night. Well after too many pints of beer, three coins and three fag packets down the boozer with some mates. Let's see if I can put it into English ...

The fact that Paul S knows where the prize is is key to this teaser. If he didn't, then 1/3 of the time he would open the door with the 500 which messes up the plot.

Paul knows he can always reveal a loosing door to you - he will have at least one, and possibly two, to choose from. Your chance of getting the right door first time is 1/3. Alternatively, Paul's chance of keeping his 500 is 2/3 if you stick with your choice.

1/3 of the time when you pick your door, Paul groans silently at the thought of loosing another 500. He wants to tempt you away so he makes you the offer. You switch, Paul cheers (silently) knowing that both of his doors were duff.

2/3 of the time when you pick your door, Paul is happy 'cos he knows there is nothing there. But he's also worried because he's got the 500, and the quiz rules state he must show you an empty door and offer you the chance to switch. By taking him up, you are effectively swapping your 1/3 chance of walking off with the 500 with his 2/3 chance of keeping the 500. And to add insult to injury, he's helped you by showing you where it is.

This is a better explanation and it's just occurred to me: look from another point of view. Who would you rather be most of the time? 1/3 of the time you've got the 500, 2/3 of the time he's got it. If he offers you to swap his two doors for your one, you'd be mad to turn him down - you get two bites at the cherry. Especially if you can guarantee to pick the prize from his two doors for the 2 out of 3 times he really does have it. And you can, because he's helped you by showing you which of his two doors is a looser. So on the 2 out of 3 times he's got the 500, you are guaranteed to win it becuase he must show you an empty door.

I think this makes sense ...

Answer the following 10 questions IN NO MORE THAN
2 MINUTES - NO CHEATING!!!

1. Do they have 5th November in America?
2. Some months have 30 days, some have 31 days. How many months have 28 days?
3. If you had only one match and entered a dark room where there was an oil lamp, an oil heater and some kindling wood, which would you light first?
4. If the doctor gave you three pills and told you to take one every half hour, how long will they last?
5. A man built a house with four sides, a rectangular structure, each side having a southern exposure. A big bear came toddling by, what colour is the bear?
6. A farmer has 17 sheep - all but 9 died. How many sheep did he have left?
7. Divide 30 by half, add 10. what is your answer?
8. Take two apples from three apples. What do you have?
9. How many animals of each species did Moses take into the ark?
10. If you drive a bus with 17 people on it from London and stop in Birmingham to pick up 9 more and drop off 5 passengers, and at Manchester you drop off 7 more and pick up 6 and arrive in Leeds 5 hours later, what is the name of the driver?

All done. That two minutes went quick!!!

I'll post the answers soon!

STEVED

It certainly does to me......now suppose Paul S has no idea which door hides the NAP500.........

Cheers

Don

[This message was edited by Don Atkinson on WEDNESDAY 28 November 2001 at 23:02.]

Cheers

Don

PS Looks like it worked. So if you don't want to know the answer yet, don't peek!!!

[This message was edited by Don Atkinson on WEDNESDAY 28 November 2001 at 23:01.]

The question is - Do they have a strategy that ensures them some minimum of right guesses ?

I haven't given this much thought yet but can see that if they agree before hand that numbers 1,2,3 and 4 will each will call out the colour of the hat of the man 4 places in front, then at least 5,6,7 and 8 will get theirs right.

But I will think about this a bit more

Cheers

Don

Sam who?????.....I'm curious

Appologies Steve, I forgot you posted the answer above and then held back on the solution. When Bam failed to get his post to work i thought i would post my solution. My daughter got this on a 'management' course recently and phoned for the answer and wouldn't put the phone down until i'd worked it out for her! Is your solution more 'elegant' ?

Cheers

Don

Sam Loyd (sorry about the incorrect spelling last time) was a famous American who devised over 10000 puzzles in his lifetime. Some of them have become classics, redressed in various forms. "How far to salisbury" is the old Sam Loyd ferryboat problem, which you have cleverly re-naimed. It is a classic Sam loyd problem in that it has an elegant solution, as well as being able to be solved by more laborious or complex maths.

The "elegant" solution is as follows:-

The distance between the two places is "X".

When the vans first meet, vanA (which set off from the dealer) has travelled 30 miles. The total distance travelled by both vans is X.

When the vans meet again, the total distance travelled by both vans is 3X, and therefore vanA must have travelled 90 miles in total.

We know that VanA travelled X plus 15 miles; therefore X must be 75 miles.

Very neat!

There are many other Sam Loyd problems accessible on the web.

Steve D

quote:

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Can you expand the reasoning on that one please??

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For every combined distance X trvelled by the vans, VanA is responsible for 30 miles. So at 3X combined distance travelled, it is responsible for 90 miles. The rest follows on ...

That is a very neat solution! So much for my simultaneous equations!

Still too tricky?

They're all in a queue. Presumably an event of some sort - a religous ceremony or a football match say.

They are all given the same colour hat to differentiate them from other groups?

Or, the hats contain a mirror or other reflective surface (eg motor cycle helmet).

Otherwise, it must be a trick!!!!

STEVED

Here are the answers:-

1) Yes they do have 5th November (but they don't celebrate Guy Fawkes).
2) All months have 28 days (some have more!).
3) You would light the match first.
4) The pills last one hour (eg 1:00, 1:30, 2:00).
5) White (polar bear - he is on north pole).
6) 9 (all BUT 9 died).
7) 70 (divide 30 by half = 60, plus 10).
8) 2 apples (you TOOK 2 apples).
9) None (Moses didn't take any animals, Noah did!)
10) Your own name (If YOU drive a bus .....!)

I was given this test on a training course, as light relief. Two minute time limit is strictly applied. The tutor said that he always gives this test after lunch to get brains back into gear. In all the years he has done it, NO-ONE has ever got 10 out of 10. I got 8 out of 10 (failed on 8 and 9!)

STEVE D

First divide the balls into 3 sets of 4.
Then weigh one set against another (A). If they balance you know the remaining set of 4 contain the odd ball (skip the next paragraph).

When A is imbalanced you can identify 4 as heavy (H) candidates and 4 as light (L) candidates. The remaining 4 are all "good". Now weigh 2 H and one L against 3 good balls (B). If the 3 candidate balls are heavy you compare the two H candidates (C) to find the odd ball. If the 3 candidate balls are light you have found the odd, L ball. If the 3 candidates balance then EITHER the remaining H is heavy or one of the remaining 2 Ls is light. Compare the 2 Ls (D) and if they balance you know the spare H is heavy otherwise you know which is light.

If the weighing A balanced, you know the other set of 4 contains the odd ball. Take 3 of them and compare with 3 good balls (E). If they balance the spare ball is odd and you must compare with a good ball to determine whether it is heavy or light (G). If they do not balance then you have 3 that you know are either heavy or light. Compare any 2 of them (F) to find the odd ball. If they balance the spare is the odd ball.

Phew! Still prefer my first solution with 4 weighs: much simpler to describe!!

I was unable to open your mspaint attachment (because I don't have mspaint!!)therefore I have had to visualise your explanation, which is slightly different to my own solution.

You say If the 3 candidates balance then EITHER the remaining H is heavy or one of the remaining 2 Ls is light.

At this point in your explanation however, you seem to have 2H remaining and 3L remaining. Have I mis-understood your explanation, and is it important?

Cheers

Don

quote:

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Originally posted by Don Atkinson:
PS Looks like it worked. So if you don't want to know the answer yet, don't peek

---

Don,

I peeked, but couldn't read the graphic.

This sort of thing should really be saved as a GIF rather than JPG. This is much more suitable for this type of image (line art).

You'll probably find it is smaller as well as much more legible.

Still, I think I've picked up enough to see what I missed from the question - I couldn't see why the distances were different in the two directions.

cheers, Martin

Divide balls into 3 groups of 4
Weigh two of them (A). If they balance go to E. Otherwise you now have 4 candidate heavy balls (H) and 4 candidate light balls (L) and 4 good balls (shown in green).

Now weigh 1H and 3L vs 1L and 3 good (B). This leaves 3 H spare. If it balances the spare 3H are heavy ->go to D. If it doesn't balance you either have the H and L balls so go to C or 3L balls so go to D.

(E) You have 4 unknown balls. Weigh 3 vs good and keep one spare. If balance the spare is odd and you need to determine whether it is heavy or light (F). Otherwise you have 3 that you know are either heavy or light so go to D.

(D) If you have 3 balls and you know whether they are heavy or light you can find the odd one.

That's it.
Can I go to bed now???

Now your concience is clear, I bet you slept better after that!!!

Cheers

Don