A Fistful of Brain Teasers

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)

"laid-back-but-awfully-reassuring"

Original Post

Far from being short-changed.....

A man pops into a bank and cashes a cheque. He pockets the money without examining it.

Shortly after, he spends half a crown (2s – 6d).

He realises that he now possesses twice as much cash as the amount on his cheque and that the cashier had inadvertently given him £££s for shillings and shillings for £££s.

He didn’t have any other cash and he hadn’t disposed of any of the cash from the cheque, other than the half a crown.

What was the amount on the cheque ?

simon, but not simple posted:

Is the answer 15.75 miles?

You walk uphill for 5.25 hours @ 1.5 mph = 7.875 miles

Your walk down for 1.75 hours @ 4.5 mph = 7.875 miles

Or is it one of those trick questions?

Not a trick question, just plain, simple arithmetic or algebra will get the answer.

I have to admit, I had to put it down on paper, rather than doing it in my head. I kept muddling the 1½; 4½ and 6.

Another distraction from work……….

I popped out to the local shop this morning with a certain amount of money. I spent half of it and realised that I now had in my possession just as many shillings as I previously had pounds, and half as many pounds as I had previously had shillings..

How much money had I spent ?

Don Atkinson posted:
simon, but not simple posted:

Is the answer 15.75 miles?

You walk uphill for 5.25 hours @ 1.5 mph = 7.875 miles

Your walk down for 1.75 hours @ 4.5 mph = 7.875 miles

Or is it one of those trick questions?

Not a trick question, just plain, simple arithmetic or algebra will get the answer.

I have to admit, I had to put it down on paper, rather than doing it in my head. I kept muddling the 1½; 4½ and 6.

DOH!! Serves me right for looking at this instead of working

Nick from Suffolk posted:

9 pounds 19shillings (originally 19/18, leaving 9/19), that was easier than the first. Yes, I am very bored with proof-reading my report. Perhaps I should fire up the system

Ah ! Proof-reading...............zzzzzzzz!!!!!!!!!

Naim music and the Naim Forum are far more enjoyable, but not profitable !

Now that Simon has got the grey matter into gear I can confirm your £-s-d are in as good shape as the Speed, Time, Distance.

Double your money whilst not working.............

If you double £6–13s you get £13–6s, ie the pounds and the shillings merely change.

Can you find another sum of money (£-s-d, but without the pence) in which the pounds and shillings likewise change when the lesser is multiplied by a positive integer (eg 2, 3, 4, 5 etc etc) to give the larger sum ?

Don Atkinson posted:

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 !

The £sd or sometimes lsd (that fell out of favour I suspect down  to the drugs connotation) was from the Roman currency names, in Latin they were Librae, Solidi and Denarii, the S was just a coincidence. (I always knew I'd use my O'Level Latin one day.)

But the counting system, 12d to 1s and 20s to £1 is very non-Roman. Factor in the concept of a Guinea, as well.

Proof-reading is dull (but necessary and I know my place in the system), but throw out a different challenge.

If £M-Ns-0d then it is necessary to solve for M and N, given n,

 (20n-1)N = (20-n)M or M/N = (20-n)/(20n-1)

Not sure whether there is anything other than the sledgehammer route. That is even duller to solve than to undertake my proof reading. 

Eoink posted:
Don Atkinson posted:

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 !

The £sd or sometimes lsd (that fell out of favour I suspect down  to the drugs connotation) was from the Roman currency names, in Latin they were Librae, Solidi and Denarii, the S was just a coincidence. (I always knew I'd use my O'Level Latin one day.)

I knew I should have continued with Latin, rather than concentrating on History and Geography.........

..............and now I know why

Cheers Eoink !!

Nick from Suffolk posted:

But the counting system, 12d to 1s and 20s to £1 is very non-Roman. Factor in the concept of a Guinea, as well.

Proof-reading is dull (but necessary and I know my place in the system), but throw out a different challenge.

If £M-Ns-0d then it is necessary to solve for M and N, given n,

 (20n-1)N = (20-n)M or M/N = (20-n)/(20n-1)

Not sure whether there is anything other than the sledgehammer route.That is even duller to solve than to undertake my proof reading. 

I'm so pleased to have brightened up your day such that proof reading seems to be exciting after all

I can't recall whether I use a sledgehammer or something more subtle to crack that one ! I think I might have used  a spreadsheet.

But I do recall finding only one solution other than 2 x £6-13s = £13-6s

Don Atkinson posted:
Nick from Suffolk posted:

But the counting system, 12d to 1s and 20s to £1 is very non-Roman. Factor in the concept of a Guinea, as well.

Proof-reading is dull (but necessary and I know my place in the system), but throw out a different challenge.

If £M-Ns-0d then it is necessary to solve for M and N, given n,

 (20n-1)N = (20-n)M or M/N = (20-n)/(20n-1)

Not sure whether there is anything other than the sledgehammer route.That is even duller to solve than to undertake my proof reading. 

I'm so pleased to have brightened up your day such that proof reading seems to be exciting after all

I can't recall whether I use a sledgehammer or something more subtle to crack that one ! I think I might have used  a spreadsheet.

But I do recall finding only one solution other than 2 x £6-13s = £13-6s

Hi Don

I think £2 17s with a multiplicative factor of 6 will do it.  And I think this is the only other solution.

Roger

Peakman posted:
Don Atkinson posted:
Nick from Suffolk posted:

But the counting system, 12d to 1s and 20s to £1 is very non-Roman. Factor in the concept of a Guinea, as well.

Proof-reading is dull (but necessary and I know my place in the system), but throw out a different challenge.

If £M-Ns-0d then it is necessary to solve for M and N, given n,

 (20n-1)N = (20-n)M or M/N = (20-n)/(20n-1)

Not sure whether there is anything other than the sledgehammer route.That is even duller to solve than to undertake my proof reading. 

I'm so pleased to have brightened up your day such that proof reading seems to be exciting after all

I can't recall whether I use a sledgehammer or something more subtle to crack that one ! I think I might have used  a spreadsheet.

But I do recall finding only one solution other than 2 x £6-13s = £13-6s

Hi Don

I think £2 17s with a multiplicative factor of 6 will do it.  And I think this is the only other solution.

Roger

Well-done that man ! Sure, £2-17s multiplied by 6 gives £17-2s and satisfies the quest.

And it was the only solution I could find using the spreadsheet/sledgehammer approach.

(Un)conditional Love............

I persuaded my grandson to be good towards his mum for a month (30 days) in return for 8 shillings per day on the condition that for every day that he wasn’t good (ie rotten) towards his mum he would forfeit 10 shillings per day.

At the end of the month we broke even, which was a disaster because it convinced my grandson that it wasn’t worth being good towards his mum !

So, how many days was he good to his mum and how many days was he rotten.

We had agreed that the daily rates of reward and forfeit would be pro-rata for those days when he was partly good and partly rotten.

Don Atkinson posted:
steved posted:

Good 13.333days, Bad 16.667 days?

Cheers, Steve D

Steve,

youv’e done the hard work, but...........

cheers, Don

Is this a pedantic one where we don’t know. He could have been nice and nasty on each of the thirty days as it’s pro-rataed, through to I think good  on 14 days minimum. 

Eoink posted:
Don Atkinson posted:
steved posted:

Good 13.333days, Bad 16.667 days?

Cheers, Steve D

Steve,

youv’e done the hard work, but...........

cheers, Don

Is this a pedantic one where we don’t know. He could have been nice and nasty on each of the thirty days as it’s pro-rataed, through to I think good  on 14 days minimum. 

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

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.

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 !

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............

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….

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.

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

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 ?

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