Author Topic: Arithmetic that makes you cringe  (Read 14725 times)

Tim Hall

  • I want to eat the fleeting shade of your lashes
Re: Arithmetic that makes you cringe
« Reply #150 on: January 30, 2020, 07:51:29 am »
43 is the largest number of Chicken McNuggets which couldn't be made using the standard sized packs (6, 9, 20).

This reminds me of a rather neat problem I recall from my primary school teaching days.

A 40kg weight drops on the floor and breaks into 4 pieces. It so happens that the pieces are precisely the correct mass to allow any number of whole kilograms from 1 to 40 to be weighed on a balance. What is the mass of each of the 4 pieces?
I've been chewing this over while fooling up and down the motorways of this fair land.
A series of (2^n)-1 sort of works, in that, for example pieces with masses of 1,3 , 7 and 15 kg allow you to get any of 1 to 26kg (I think). However it fails on the totalling 40kg front.
There are two ways you can get exercise out of a bicycle: you can
"overhaul" it, or you can ride it.  (Jerome K Jerome)

Giraffe

  • I brake for Giraffes
Re: Arithmetic that makes you cringe
« Reply #151 on: January 30, 2020, 08:40:53 am »
'Reduces the temperature by 20%' using deg. F - that could get tricky. OK if R or K used.
2x4: thick plank; 4x4: 2 of 'em.

Wowbagger

  • Dez's butler
    • Musings of a Gentleman Cyclist
Re: Arithmetic that makes you cringe
« Reply #152 on: January 30, 2020, 09:40:14 am »
43 is the largest number of Chicken McNuggets which couldn't be made using the standard sized packs (6, 9, 20).

This reminds me of a rather neat problem I recall from my primary school teaching days.

A 40kg weight drops on the floor and breaks into 4 pieces. It so happens that the pieces are precisely the correct mass to allow any number of whole kilograms from 1 to 40 to be weighed on a balance. What is the mass of each of the 4 pieces?
I've been chewing this over while fooling up and down the motorways of this fair land.
A series of (2^n)-1 sort of works, in that, for example pieces with masses of 1,3 , 7 and 15 kg allow you to get any of 1 to 26kg (I think). However it fails on the totalling 40kg front.

1 & 3 are correct. However, 7 is unnecessarily small as it allows 2 ways of reaching 4 (3+1 and 7-3)...
Eating's a serious business. Don't bollocks around wagging your tail.

Re: Arithmetic that makes you cringe
« Reply #153 on: January 30, 2020, 10:59:50 am »
It's 3^n.

1, 3, 9, 27 work.

Re: Arithmetic that makes you cringe
« Reply #154 on: January 30, 2020, 11:08:22 am »
It's not really 'arithmetic that makes you cringe' but this is a nice problem nonetheless...

There are 1000 numbered lockers in a line.  All of them are closed.
First, you pass along the line, changing the door position (i.e. opening!) every door.
Then, you go back to the start, changing the door position (i.e. closing) every even-numbered door.
Then you go back to the start, changing the door position of every third door (i.e. closing door 3, opening door 6, closing door 9...).
Then you go back to the start, changing the door position of every fourth door.
Then every fifth door.
...
... Lastly, change the door position of door 1000.

How many doors are open, and how many are closed?

Wowbagger

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Re: Arithmetic that makes you cringe
« Reply #155 on: January 30, 2020, 11:10:31 am »
It's 3^n.

1, 3, 9, 27 work.

Correct!
Eating's a serious business. Don't bollocks around wagging your tail.

Re: Arithmetic that makes you cringe
« Reply #156 on: January 30, 2020, 11:29:03 am »
How many doors are open, and how many are closed?

Ah yes, I remember this one.

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"Yes please" said Squirrel "biscuits are our favourite things."

Wowbagger

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Re: Arithmetic that makes you cringe
« Reply #157 on: January 30, 2020, 11:42:51 am »
Yes, of course. They are the only numbers that have an odd number of factors.
Eating's a serious business. Don't bollocks around wagging your tail.

Tim Hall

  • I want to eat the fleeting shade of your lashes
Re: Arithmetic that makes you cringe
« Reply #158 on: January 30, 2020, 12:08:03 pm »
It's not really 'arithmetic that makes you cringe' but this is a nice problem nonetheless...

There are 1000 numbered lockers in a line.  All of them are closed.
First, you pass along the line, changing the door position (i.e. opening!) every door.
Then, you go back to the start, changing the door position (i.e. closing) every even-numbered door.
Then you go back to the start, changing the door position of every third door (i.e. closing door 3, opening door 6, closing door 9...).
Then you go back to the start, changing the door position of every fourth door.
Then every fifth door.
...
... Lastly, change the door position of door 1000.

How many doors are open, and how many are closed?
These lockers. Are they in the cloakroom at Hilbert's hotel?
There are two ways you can get exercise out of a bicycle: you can
"overhaul" it, or you can ride it.  (Jerome K Jerome)

Re: Arithmetic that makes you cringe
« Reply #159 on: January 30, 2020, 01:28:45 pm »
Hehe!

Another lovely problem:

A man is in a rowing boat in the middle of a pond.  He takes a large rock from the bottom of the boat and drops it into the water, whereupon it sinks.  What happens to the level of the water in the pond?

Re: Arithmetic that makes you cringe
« Reply #160 on: January 30, 2020, 01:39:53 pm »
Same volume of water displaced whether the rock is on the bottom or in the boat, so no change?

Kim

  • Timelord
Re: Arithmetic that makes you cringe
« Reply #161 on: January 30, 2020, 01:43:05 pm »
Surely the displacement required to support the rock is greater than the volume of the rock, as it's more dense than water.  On that basis, the water level goes down?
Careful, Kim. Your sarcasm's showing...

Re: Arithmetic that makes you cringe
« Reply #162 on: January 30, 2020, 01:49:01 pm »
That looks MUCH better!

Re: Arithmetic that makes you cringe
« Reply #163 on: January 30, 2020, 03:34:32 pm »
Kim has it.  It's a little counterintuitive!

Re: Arithmetic that makes you cringe
« Reply #164 on: January 30, 2020, 03:38:31 pm »
Thanks, Legs. Yes, a lovely problem.

Brain now updated (I hope).

Re: Arithmetic that makes you cringe
« Reply #165 on: February 03, 2020, 04:15:41 pm »

Basil

  • Um....err......oh bugger!
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Re: Arithmetic that makes you cringe
« Reply #166 on: February 03, 2020, 07:32:40 pm »
I was expecting that would convert to a nice round number of feet or yards.  But it doesn't. 
That's the usual reason for decimals of that precision in press reports.

So, we can expect a cow to be arrested some time soon.
Quote from: Kim
And remember that friends who organise things on Facebook aren't proper friends anyway.

Wowbagger

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    • Musings of a Gentleman Cyclist
Re: Arithmetic that makes you cringe
« Reply #167 on: February 03, 2020, 07:36:57 pm »
This image of Gerald Corrigan's house shows where North Wales Police believe the shooter was located


A triumph of precision over accuracy.
[/quote

Was that the case of the bloke who got shot by someone with a crossbow?
Eating's a serious business. Don't bollocks around wagging your tail.

Phil W

Re: Arithmetic that makes you cringe
« Reply #168 on: February 03, 2020, 07:48:30 pm »
Hehe!

Another lovely problem:

A man is in a rowing boat in the middle of a pond.  He takes a large rock from the bottom of the boat and drops it into the water, whereupon it sinks.  What happens to the level of the water in the pond?

The large rock penetrates the pond lining and completely empties it of water, leaving the man and boat on a muddy slimy bottom.

Re: Arithmetic that makes you cringe
« Reply #169 on: February 03, 2020, 08:05:58 pm »
^^^^^^^^^ I was asked that question in interview with Vosper Thorneycroft back when the world was young (about 1987).  The difference was that it was a large ship, a very small very heavy weight, and a dockyard basin.  A question in logical thinking.  They are probably not allowed to ask things like that these days.

Re: Arithmetic that makes you cringe
« Reply #170 on: February 14, 2020, 12:34:06 pm »
Surely the displacement required to support the rock is greater than the volume of the rock, as it's more dense than water.  On that basis, the water level goes down?

Your right I think. The size of the rock is immaterial to the displacement needed by the boat to support but it its weight is.  An empty steel box 1m3 would displace much less than a box the same size filled with something really dense like lead or gold. Drop them in the water and they both displace 1m3 of water no matter what their weight is. When its on the boat its a weight problem when its in the water its a volume problem.
I think you'll find it's a bit more complicated than that.