A Fistful of Brain Teasers

Posted by: Don Atkinson on 13 November 2017

A Fistful of Brain Teasers

For those who are either non-British, or under the age of 65………. The UK used to have a brilliant system of currency referred to as “Pounds, Shillings and Pence”. Simplified to £ ? s ? d. No! Don’t ask me why the “Pence” symbol is a “d”, just learn it and remember it !

A £ comprised 20 Shillings and a Shilling comprised 12 Pence. Thus a £ comprised 240 Pence. I reckon that both Microsoft and Apple would have difficulty with these numbers in their spreadsheets, more so if we included Guineas, Crowns, Half-Crowns and Florins. However, I digress..............

The purpose of the explanation is to assist with the first two or three teasers that follow. So just to ensure a reasonable comprehension has been grasped…. ….. if each of three children has £3 ? 7s ? 9d, then collectively they have £10 ? 3s ? 3d   Got the idea ? Good ! Just try 5 children, two each with £4 ? 15s ? 8d and three each with £3 ? 3s ?  4d. How much do they have between them ? (this isn’t the first brain teaser, just the basic introduction with some “homework”, the Teasers follow)

Posted on: 15 November 2017 by steved

Doh! My answer got my "good" and "bad" the wrong way round! It should have read Good 16.667, Bad 13.333. It is a lesson in life that good work is often let down by bad carelessness.......

Posted on: 15 November 2017 by Eoink
Don Atkinson posted:
 

 

 

 

Hi Eoink,

It's not meant to be pedantic, and I hope it isn't.

It doesn't matter whether he's good for part of each and every day, or good for the first part of the month then rotten for the rest, or simply good and bad at random.

But 13.333 x 8 shillings doesn't = 16.667 x 10 shillings so can't be the correct answer.

I sometimes think, that as we get older we read these simple maths questions with a cynical, semi-political outlook. eg where's the catch ?; do the words have a hidden meaning ? and we challenge poorly-worded or slightly ambiguously worded questions.

This one was meant to be simple. How do you divide 30 such that "A" x 8 = "B" x 10.

The story-line is the "teaser" part. ie can you unravel the story......

Hope this helps

Sorry Don, I saw what I’d written and realised it sounded negative when I meant anything but, but when I went to edit it, I’d missed the 15 minute window. I’m really enjoying these, I don’t have enough time usually to do them first, so I don’t read down and see other people’s answers. On this one I’d done the “hard sums”, recognised the numbers as be8ng what I’d got and didn’t spot the swap, so was trying to think what was the possible tweak, rather than reading carefully.

i’m genuinely sorry I sounded negative, it was very sloppy writing on my part, apologies again.

Posted on: 15 November 2017 by Don Atkinson
steved posted:

Doh! My answer got my "good" and "bad" the wrong way round! It should have read Good 16.667, Bad 13.333. It is a lesson in life that good work is often let down by bad carelessness.......

Yes, that's life.....................

..............got there in the end !

Posted on: 15 November 2017 by Don Atkinson
Eoink posted:
Don Atkinson posted:
 

 

 

 

Hi Eoink,

It's not meant to be pedantic, and I hope it isn't.

It doesn't matter whether he's good for part of each and every day, or good for the first part of the month then rotten for the rest, or simply good and bad at random.

But 13.333 x 8 shillings doesn't = 16.667 x 10 shillings so can't be the correct answer.

I sometimes think, that as we get older we read these simple maths questions with a cynical, semi-political outlook. eg where's the catch ?; do the words have a hidden meaning ? and we challenge poorly-worded or slightly ambiguously worded questions.

This one was meant to be simple. How do you divide 30 such that "A" x 8 = "B" x 10.

The story-line is the "teaser" part. ie can you unravel the story......

Hope this helps

Sorry Don, I saw what I’d written and realised it sounded negative when I meant anything but, but when I went to edit it, I’d missed the 15 minute window. I’m really enjoying these, I don’t have enough time usually to do them first, so I don’t read down and see other people’s answers. On this one I’d done the “hard sums”, recognised the numbers as be8ng what I’d got and didn’t spot the swap, so was trying to think what was the possible tweak, rather than reading carefully.

i’m genuinely sorry I sounded negative, it was very sloppy writing on my part, apologies again.

Hi Eoink,

No need to apologise, it didn't sound negative to me, I've mis-typed a few questions in the past, or omitted a key feature, A few people have had to ask me to clarify things.

Main thing is to get the old grey matter going again and to enjoy a puzzle without any deadline or consequence............

Posted on: 15 November 2017 by Don Atkinson

Cyclists !!!!!!!!!!!!!!!!!!!

Riding his new bicycle, winky rode 1 mile in three minutes with the wind at his back, but it took him 4 minutes to cover the return mile with the same wind against him.

How long would it take him to ride the same mile in nil-wind conditions.

You can assume the route is level and that road friction is the same in each direction etc etc etc….

Posted on: 15 November 2017 by u77033103172058601

I rather like the hoary old chestnut. Which group of numbers is more numerous

All the rational numbers between 0 and 1; a rational is any number expressible as a fraction of 2 real numbers, 2/3, 4/5, 9994/1111272 etc

All the irrational numbers between 0 and 1; an irrrational cannot be expressed as a fraction, rather as an infinite decimal (a bit difficult to give an example, except for pi and e, albeit those aren't less than 1, so to conform with my 0 to 1, that would be (pi - 3) and (e-2))

Fascinated me over 40 years ago and I still find it fascinating today. Although I did hear, but have yet to track down, that there has been a new insight into this in the last few months.

Yes, I am still plagued by proof-reading today. It's a report I wrote and I have to resist tweaking the words.

Posted on: 15 November 2017 by steved

With fingers crossed for no carelessness this time, I get the answer as 3.429 minutes (or 60/17.5). 

Posted on: 15 November 2017 by Don Atkinson
steved posted:

With fingers crossed for no carelessness this time, I get the answer as 3.429 minutes (or 60/17.5). 

I think you can relax steve ! (24/7)

Posted on: 15 November 2017 by Don Atkinson

If a hen and a half lay an egg and a half in a day and a half, how many and a half who lay better by half will lay half a score and a half in a week and a half ?

If anybody needs to clarify any aspect of this teaser just ask……………eg "half a score and a half" = 10½

Posted on: 15 November 2017 by TOBYJUG

That old chestnut.

Three friends out shopping.  One sees a shirt for £97. But has run out of cash. The other two both help out by both offering £50. She goes on to buy the shirt and borrowing the funds. With the change of £3 she gives £1 each to the others and keeps £1 for herself.

The next day she gives £49 to each of her friends.

Later in the week mulling it over, she thinks.. she gave out £100 and kept £1.   How did she end up paying £99 for a £97 shirt ?

Posted on: 15 November 2017 by Don Atkinson

She only had to withdraw 2 x £49 = £98 from her (piggy) bank to refund her friends. She could easily have paid the (kept) £1 into her (piggy) bank thus recognising that her net withdrawal (and expenditure) was £98 - £1 = £97

Nice one, Toby !

Posted on: 15 November 2017 by JRHardee

Five days of good behavior are cancelled by four days of bad behavior. The kid is bad 4/9 of the 30 days and good the other 5/9. 

Posted on: 15 November 2017 by Don Atkinson
JRHardee posted:

Five days of good behavior are cancelled by four days of bad behavior. The kid is bad 4/9 of the 30 days and good the other 5/9. 

That's a very elegant way of explaining the solution.

Cheers

Don

Posted on: 15 November 2017 by Don Atkinson

Age of uncertainty

If you add the square of Andrew’s age to the age of Anne you get 62.

If you add the square of Anne’s age to the age of Andrew you get 176.

How old are Andrew and Anne ?

Posted on: 15 November 2017 by Eoink

Andrew is 7 and Anne is 13.

Posted on: 16 November 2017 by steved

Agreed with Eoink. An interesting puzzle in that solving the equations "mathematically" quickly gets complicated, but the solution easily yields when the range of possible solutions is investigated.

Posted on: 16 November 2017 by Don Atkinson
steved posted:

Agreed with Eoink. An interesting puzzle in that solving the equations "mathematically" quickly gets complicated, but the solution easily yields when the range of possible solutions is investigated.

That’s what I felt. It took a while to realise that the range is limited by  “squares” less than 62.

Posted on: 16 November 2017 by Eoink
Don Atkinson posted:
steved posted:

Agreed with Eoink. An interesting puzzle in that solving the equations "mathematically" quickly gets complicated, but the solution easily yields when the range of possible solutions is investigated.

That’s what I felt. It took a while to realise that the range is limited by  “squares” less than 62.

Exactly, it's a very clever question. You look at it for a while trying to find a general solution, decide that brute force is the only practical way, sigh and get ready for a slog, then look at the 62 and realise it's a very manageable set, especially if like me you start at 7 to work down.

Posted on: 16 November 2017 by Eoink

Maybe we should add a stipualtion to challenge Don, the numbers must all be Naim amplifier models (the thought being sparked by the 62 in the one above). So 12, 22, 32, 32.5..., 90, 110, 135...

 

Actually thinking about it, that'll be pretty limiting, apart from the S1s I think all preamps will end with 2 and most if not all power amps are multiples of 5 with the majority being multiples of 10.

Posted on: 16 November 2017 by Don Atkinson

Motorists !!!!!!!!!!!!!

Myself and Mrs D were walking along a country lane on Tuesday (one of my days off) at a steady 3½ mph when a car overtook us, missing Mrs D by inches !

“Cricky !” said Mrs D, somewhat disturbed. (well, I think she said Cricky !) “He must have been doing 60mph or more !”

“Oh! I doubt it” said I, appreciating that most motorist are very considerate towards pedestrians (it’s a storey – not reality !!!) “We have only taken 27 steps since that car disappeared around that bend ahead. Let’s see how many more steps it takes to reach that bend”

“135”, said I, as we reached the point at which the car had disappeared.

“So what ?” asked Mrs D.

“Well, I can now tell you how fast that car was travelling, assuming it was going at a steady speed”

“And……………?” asked Mrs D

Posted on: 16 November 2017 by u77033103172058601

24.5mph, but I have finished my proof reading and drunk nearly 2 bottles of wine, at a cost great than the MAP proposed limit. I will leave you to ascertain which is more wrong.

Posted on: 17 November 2017 by Don Atkinson

“We have only taken 27 steps since that car disappeared around that bend ahead. Let’s see how many more steps it takes to reach that bend”

I think I could have worded this part more clearly. From the time the car passed us, to the time it disappeared around the bend, we had taken 27 steps at 3½ mph.

It took us a further 135 steps to reach the bend.

Posted on: 17 November 2017 by Eoink

Ah, in that case, I make it 21mph. (And thanks for the 135 in the question, much appreciated.)

Posted on: 17 November 2017 by Don Atkinson

Trains !!!!!!!!!!!!!!!!

Myself and Mrs D travelled by train from Newbury to Milchester last week and an hour after leaving Newbury something went wrong with the train.

We had to continue the journey at three-fifths of the earlier speed and it made us two hours late at Milchester.

The Conductor mentioned that if the fault had developed 50 miles further on, the train would have arrived 40 minutes sooner.

How far is it from Newbury to Milchester ?

Posted on: 18 November 2017 by Peakman
Don Atkinson posted:

Trains !!!!!!!!!!!!!!!!

Myself and Mrs D travelled by train from Newbury to Milchester last week and an hour after leaving Newbury something went wrong with the train.

We had to continue the journey at three-fifths of the earlier speed and it made us two hours late at Milchester.

The Conductor mentioned that if the fault had developed 50 miles further on, the train would have arrived 40 minutes sooner.

How far is it from Newbury to Milchester ?

Hi Don

I think the distance is 200 miles and the train started at 50mph.

Only 2 hours late sounds pretty good by our local standards.

Roger