Brain Teasers are Back!

No need to draw the line or post a picture, just list the seven shapes in sequence.

This one came out of my ‘O’-Level book. So should suit the 14-15 year old gamblers !

I have a bag containing 12 discs, some of which are red. If I were to add 3 red discs to this bag, my chance of selecting a red disc at random would be doubled.

How many red discs are there in the bag ?

2?

2/12 = 1/6 of the first bag

Add 3 red, then 5/15 = 1/3, twice 1/6.

1 Like

Ah ha! Nicely explained.
I presume you used the tried and tested “Trial & Error” method ie 1/12: 4/15 didn’t work but 2/12; 5/15 did ?

Or did you go the more subtle route of 2x/12 = (x+3)/15 ?

Or perhaps some other technique ?

Either way, well done.

1 Like

A couple more for the gamblers …… first …

What is the chance of throwing a six (using a fair dice) if you are given 6 throws ?

…and secondly …

Two people, let’s call them Mike and Eoink, play a game by rolling two fair dice. The first to roll a double six wins. If Mike goes first what is the probability that :-
a) Eoink wins on his first throw
b) Mike wins on his second throw

I did, mainly because I didn’t have pen and paper to hand.

1 Like

I don’t know but I’d be checking the dice.

a), 2/36 or 1 in 18
b), 3/36, or 1 in 12

Assuming the probability is defined from the start of the game, otherwise it’s just the roll of the dice and 1 in 36 each roll.

The dice are mathematically fair.

Mike and Eoink might not be, but the dice are guaranteed :sunglasses:

2 Likes

Ah !

The quextion is based on the specification of the game. Mike and Eoink take turns at rolling the dice until one of them throws a double six
.
Mike goes first. If he throws 2x6, he wins. So the probabilty that Eoink wins on his first throw will be zero, because the game didn’t get that far. ie it stops when somebody throws (6:6)

But if Mike throws (1:4) or any combination other than (6:6), then of course Eoink gets his first throw and might throw (6:6) in which case Eoink wins on his first throw and the game stops. ie Mike has to fail to throw (6:6) on his first go AND Eoink has to throw (6:6) on his first throw.

Hope this makes the situation a bit more clear ?

1 Like

Hi Don,
I have the first four and one of the other three. Just to be sure: all letters are used and each one only once?

Hi Mulberry,

That’s correct. Each letter only once, and all 64 letters are used.

Cheers
Don

Hi Mulberry,

If you post details of your four + one shapes, it might inspire others to help out with the other two.

Probability that Mike fails to throw a double six on his first throw is 35/36
Probability that Eoink throws a double six on his first throw is 1/36

These two events are independent
So the probability that Eoink wins the game on his first throw is … ??

Shapes:-
Parallelogram, Pentagon, Triangle, Trapezium, Hexagon, Quadrilateral, Square

Looks good Steve, I couldn’t figure out how to continue after Quad.

Probably just the language barrier Mulberry. If the teasers were in German, most of us would have been foxed on the first one !

Good try.

Nicely listed Steve.

I think this caused confusion before. Is the question from when the game started, or when Eoink has his first throw. If Mike wins on his first throw, then Eoink doesn’t have a throw. So. On Eoink’s first throw, he has a 1 in 36 chance of winning.