A Fistful of Brain Teasers

Aaaaaargh! Maths again. I’m going back to the crossword.

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 ?

Last week, as usual, myself and Mrs D went for a gentle walk.

In simple terms, we walked up a hill at 1½ miles per hour and walked back down at 4½ miles per hour. In total, the walk took us 6 hours for the round trip.

How far did we walk ?

Good, a distraction from work.

Total of 13.5 miles

Cheque was 5pounds 11shillings and 6pence.

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?

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.

But that adds up to 7 hours.

Average speed is 1/2 (1/(1/1.5 + 1/4.5));  the reciprocal of the average of the reciprocal speeds. 2 1/4mph

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 ?

Nick from Suffolk posted:

Good, a distraction from work.

Total of 13.5 miles

Cheque was 5pounds 11shillings and 6pence.

Spot-on Nick. Nice work !

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

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

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.

Good 13.333days, Bad 16.667 days?

Cheers, Steve D

steved posted:

Good 13.333days, Bad 16.667 days?

Cheers, Steve D

Steve,

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

cheers, Don

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