Brain Teasers are Back!

Nice one Mike, … that should go in the ‘Best Jokes’ thread … :sunglasses:

Let’s leave this one open for a little while, just in case there are other ideas out there :sunglasses:

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Mrs R and I had two different methods (as usual). Fortunately we agreed on the answer.

Will post our solutions later. Others are free to post first of course.

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The odds of no 5 or 6 on one die is 4/6, or 2/3. The odds of no 5 or 6 on both of two dice is (2/3)**2, or 4/9. Your odds of weeding are better than even, about 55.6%

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Mrs R (who teaches probability at university) used the same approach as JR. Note that 5 and 6 related to going for a walk, so Mrs R concluded that the odds of walking is 5/9.

My approach was visual. Consider a six by six grid (e.g. like a chess board). This gives all 36 possibilities of two dice. Rows 5 and 6 and columns 5 and 6 relate to walking. Gardening is just the four by four grid that’s left. Hence gardening is 16/36 = 4/9.

If the question is worded slightly differently in that only one of 5 or 6 means walking, then squares (5,5) and (6,6) would then mean gardening. This would give 50% chance which aligns with Mike’s answer.

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Hmmm…

A 5,5 or a 6,6 is “at least one side of the dice”…… maybe my maths is better than my grammar?

This is often the case with me also. I have to read these teasers several times to ensure I am targetting the relevant problem. A bit like life in general … especially when Mrs D is involved :sunglasses:

I’d like to think that the wording was clear in this teaser.

We throw the first dice - a 5 or a 6 comes up - we go for a long walk. If a 1, 2, 3 or 4 comes up - we throw the second dice. If a 5 or 6 comes up - we go for a long walk.

Alternatively, we throw both dice together - if at least one 5 or one 6 comes up - we go for a long walk.

Two fives, two sixes or a five and a six will also satisfy the “at least” requirement.
Whether we throw the dice separately or together, no matter - the outcome is the same.

I think we can all do the arithmetic for this teaser, but as Mike says, sorting out the words needs a bit of careful thinking as well. Talking of which …

… has anyone made any progress with Willy’s sisters Fitzwilliam ? :sunglasses:

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Nice explanation, I see the errors of my ways.

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Well Darcy had a sister Fitzwilliam in Pride and Prejudice……

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Absolutely brilliant, Mike !

Jane; Mary; Kitty (Cath); Lydia
The other Bennet sisters from P&P

(Elizabeth being the star of the Bennet sisters)

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We await verification from Willy.

:+1:

Willy.

Thanks Willy.

That one is down to Mike_S

Yep, I’d seen that it was @Mike_S had solved it. My brief response was as I was multitasking, keeping an eye out for the correct tram stop.

So, only three to go, one of which should be solvable by the literary sorts amongst you. :wink:

Willy.

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I had it backwards–44% chance of weeding.

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I realise now that I’d use the method as Ravie but miscounted 18 combinations of a 5 or 6 instead of 20, so my bad :roll_eyes:

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A game of chance

Mrs D and I often play board games, cards, or dice. We have a box full of old pennies (12d = 1 Shilling, 20 shillings = £1) which we use for ‘gambling’ and ‘prize money’.

Well, yesterday she had a big win and was obviously feeling confident that luck was on her side !!

So, I offered her another wager using our two, standard, fair, six-sided dice with the usual numbers 1 to 6 on each.

For a 1,000d stake, she would roll both dice, if the sum of the numbers were greater than seven, she would win 2,000d. If not, then her stake would be lost.

Does she have a 50% (or even greater) chance of winning the wager ?

I think she has a 15/36 chance, so less than 50%.
Ravvie’s wife would know not to make the wager; Don’s wife I’m not so sure?
If you’d said greater than or equal to 7, the odds would swing in her favour (21/36).

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Mrs R used the same approach, working out the answer of 15/36 in her head. Not bad as I was interrupting her eating chocolatey chocolate cake (it’s our son’s 25th Birthday).

I just went for the following:

Symmetrical distribution of totals 2 to 12 of which 7 is in the middle. Hence less than 50% chance of 8+.

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Pre-decimalisation

It’s now just over 53 years ago since the UK and Ireland decimalised their respective currencies.

My guess is, that unless you lived in the UK and have reached that magic Senior’s Age of 60, you won’t remember our old £:s:d system, (or Pounds, Shillings and Pence)

So, either as a Teaser, or as a bit of nostalgia, Mrs D’s stake on the two dice/more than seven teaser was 1000 pence. How much was that in £:s:d. You must do this in your head, as if standing in a shop trying to decide whether a £5 note or a £10 note would be sufficient !