Brain Teaser No 1

Multiple choice questions (part 2)

In the above exam, the lowest score was -20. The highest score was 34 and the arithmetic mean (average) score was 27.

What was the least number of candidates who took the test?

Cheers

Don

Following in my footsteps

A simple set of instructions (like a computer program) might go like this....

walk five paces in a straight line
turn right 72 degrees (360 deg circle)
repeat until
back at start.

What shape will have been traced out

Cheers

Don

Yes...I know, its quite simple

a pentagon

Following in my footsteps II

Well-done to Two-sheds for getting version I

Another simple set of instructions (like a computer program) might go like this....

walk five paces in a straight line
turn right 144 degrees (360 deg circle)
repeat until
back at start.

What shape will have been traced out this time?

Cheers

Don

I imagine you would trace out a five-pointed star.

cheers

Dan

Dan,

I imagine you would trace out a five-pointed star.

You imagine right.

Cheers

Don

Following in my footsteps Part III

....so 72 deg gives a pentagon and 144 deg gives a 5-pointed star...

....any ideas about a generalised formula, or two?

Cheers

Don

and...

ther's still the unanswered teasers about muli-choice answers....

Cheers

Don

True or false

Determine which of the following statements are true and which are false

1. Exactly one of the statements in this list is false
2. Exactly two of the statements in this list are false
3. Exactly three of the statements in this list are false
4. Exactly four of the statements in this list are false
5. Exactly five of the statements in this list are false
6. Exactly six of the statements in this list are false
7. Exactly seven of the statements in this list are false
8. Exactly eight of the statements in this list are false
9. Exactly nine of the statements in this list are false
10. Exactly ten of the statements in this list are false

Cheers

Don

I think only one can be true. So all bar '9' are false.

Paul

quote:

---

Following in my footsteps Part III

....so 72 deg gives a pentagon and 144 deg gives a 5-pointed star...

....any ideas about a generalised formula, or two?

---

well formula 1:
360 / angle of turn

if this is a whole number then you will get a shape with that many sides.

Then onto the guessing, if it results in a decimal then your shape will have lines that cross each other. In this case keep multiplying the number by 2 until you get a whole number. this is the number of points your shape will have. I think I'll actually go think about this and see if I can find a decent (or prove) this solution.

Paul,

Well done, but you didn't need me to tell you that.

Cheers

Don

Two-sheds,

Good try. Keep it simple and stick with "whole number" divisors such as 72 and 144. Well....I know that 144 isn't a whole number divisor....but avoid numbers like 83....

I didn't have anything too complicated in mind

Cheers

Don

Tossing a fair coin.

OK, you have tossed a fair coin five times and called "heads" each time. On each occasion it's come down tails. You are about to toss it for the sixth time, but this time £10,000 is riding on the outcome. No cheating is involved. What should you call?

a. "tails" because the last 5 were tails.

b. "heads" because its bound to come up soon.

c. "heads" because on average it will land heads 50 % of the time, and as it has landed five times in a row on tails, it will have to land heads more in the future to achieve that 50%

d. don't worry about it, call either "heads" or "tails", whichever takes your fancy, the chances of winning are unaffected by the previous outcomes, and are therefore 50/50.

Cheers

Don

Don,

Maybe I'm missing something but if the coin is fair, and does actually have a side with a head on it, it must be 'd'. I have a feeling that there's a third door lurking somewhere though.

cheers,

Dan

Dan M,
Everything you say is true, except the last sentance.

We all really need to get over this paranoia about three doors and a couple of goats. Just act like Mrs D and always change your mind at th last moment....

Cheers

Don

Leading digits

We often see lists or tables of natural numbers (ie digits "1" through "9"), for example in profit and loss sheets, sales summaries, price lists, director's salaries etc etc. these numbers can be from as little as 1 digit long eg 5, to six-figure numbers eg 250,000, or longer, in fact, any length.

Assuming that such tables comprise RANDOM numbers, (yes, I know that in real life they aren't random, but let's assume they are) what is the probability that a number in such a table has a leading digit of 1 eg 10,600; 1,250,000;

Is it (a) 4.7%; (b) 10%; (c) 11.1%; (d) 30.1%

Cheers

Don

Leading Digits

I'd say "c" ie a 1 in 9 chance.

Steve D

Don.

Which of the following is true:

A) Your latest puzzles are getting easier
B) I'm getting smarter
C) Your latest puzzles are getting harder by appearing to be easy but in fact having an a none too obvious red herring.

Greeny,

Obviously (b) and (c)....

Cheers

Don

Steved,

As Jerremy Paxman would say on University Challenge...."nope!"

Cheers

Don

Age-old teaser

A man is 6 years older than his wife. Four years ago he noticed he had been married to her for half his life.

How old will the man be when he has been married for fifty years, if in ten years time his wife will have been married to him for two-thirds of her life?

Cheers

Don

Re-cap

and just to re-cap on an earlier teaser...

What is the probability that a natural number in a listing or table of statistics has a leading digit of 1?

Cheers

Don

Don
man is 56, wife is 50, they have been married for 30 years. When they have been married for 50 years he will be 76.

Good answer Two-Sheds

Does anybody want to post an explanation/set of formulea....

Cheers

Don