Brain Teasers are Back!

The dinner party

There are three married couples having dinner together.

George is older than Michelle’s husband.

Frank’s wife is older than Nadia.

Lynette’s husband is older than George.

Michelle is not Edward’s wife.

The oldest man is married to the youngest woman.

The oldest woman paid the bill.

Who was this ?

At the risk of looking stupid I’m going with Michelle.

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Hi Pete,

Nobody ever looks stupid in this thread !

Just people who tried and might need to try again ! and those who tried and got it right.

In this case, either we both need to try again, or we both got it right.

I’m inclined towards the latter option.

Well done !

Here’s one for the gamblers amongst us :sunglasses:

Probability

An opaque bag contains 5 red discs and 3 blue ones.

Two discs are picked out at random and not replaced.

What is the probability of getting one disc of each colour ?

15/28?

15/28 is spot-on Dozey

If you wish to outline your solution for the benefit of others, that would be great. If not, no worries, i’ll post my methodology tomorrow, unless others do so before hand.

Meanwhile, well done !

Well, there are 28 ways to pick two items (7 + 6 + 5 …). There are 15 combinations with one of each colour (5 + 5 + 5) I.e. 5 combinations (8-3) for each of the three blue items.

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Hi Dozey, nice. Being able to recognise and use combinations and/or permutations is what these are all about.

I always used to have difficulty recognising permutations or combinations and still do !

So I tend to revert to probability trees until the branches get too numerous or entangled :sunglasses:

I used a probability tree for this one …

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Starting in the top left box, draw a continuous line passing through each box once only, so that the sum of the numbers in each group of four boxes is 24.

So the first four boxes through which the line passes will add up to 24, then the next group of four boxes through which the line passes will also add up to 24 and so on.

You can post your result either by printing the diagram and scanning the resultant diagram with your drawn line. Or simply writing out the numbers in groups of four eg

6,6,3,5:
3,5,8,4: etc (which are clearly not a correct solution).

Are you sure it’s top left to start and not bottom left?

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That’s a good observation Mike !

You could actually start at quite few places, one of which is the top left and another of which is the bottom left.

In some cases you might draw the line “clokwise”, in other cases it would be “anticlockwise”.

In all the cases that I have looked at, it’s the same line.

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Variations on a theme are possible using diagonal lines - and they can even cross on the box corners, as that still has only passing once through each box:

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Neat variations IB.

Another one for the gamblers …

I have four possible routes home from work. For the first part of my journey I can either go by train or bus. The probability that I shall go by train is 2/3.

After I get off the train I can either walk or catch a bus. The probability that I shall walk is 3/4.

If the first part of my journey is by bus, then I complete my journey by taxi, with a probability of 1/5, or by walking.

What is the probability that I shall walk part of my way home ?

23/30 (I’m not very confident here, probabilities always confuse me, they don’t immediately show as a pattern to solve in my head, and I only have so many fingers to work them out on.)

Eoink,

I think you could pour yourself a celebratory glass of wine and relax in the company of Naim delivered music. Well done !

I’ll post my probability tree in a short while.

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Hi Eoink,

My probability tree below shows how I also got to 23/30.

Yep Don, same way except I ignored the non-walk paths, so didn’t have the numbers on those, multiplied and then summed in my head three times to be sure I wasn’t missing something.

Another one for the gamblers !!

An unbiased dice, marked 1 to 6, is rolled twice. What is the probability of :-

a) Rolling two sixes

b) The second throw being a six, given that the first throw was also a six

c) Getting a score of ten from the two throws

d) Throwing at least one six

e) Throwing exactly one six

No need to attempt all five subquestions. Just have a shot at any or all that you think you can manage.