JudgeMental said:

Making some not totally unreasonable assumptions, I can solve this.

The Rev Dodgson said:

JudgeMental said:

Making some not totally unreasonable assumptions, I can solve this.

I think simultaneous equations are the order of the day.

Witty Rejoinder said:

The Rev Dodgson said:

JudgeMental said:

Making some not totally unreasonable assumptions, I can solve this.

I think simultaneous equations are the order of the day.

my brane hurts already

Witty Rejoinder said:

The Rev Dodgson said:

JudgeMental said:

Making some not totally unreasonable assumptions, I can solve this.

I think simultaneous equations are the order of the day.

Or a bit of engineering trial and error :)

The Rev Dodgson said:

JudgeMental said:

Making some not totally unreasonable assumptions, I can solve this.

At least there’s no lake.

1.5 m.

Michael V said:

1.5 m.

that is a high table.

Michael V said:

1.5 m.

Let:
Amira = A
Barney = B
Table = T

1) A+T-B = 1.3

2) B+T-A = 1.7

Rearrange 1) to solve for T, 2) to solve for B.

1) T = B-A+1.3

2) B = A-T+1.7

Substitute B in equation 1).

T = A-T-A+1.3+1.7
T = -T+3
2T = 3
T=1.5

JudgeMental said:

Michael V said:

1.5 m.

that is a high table.

So is the land around Armidale.

;)

normal height of a table is around 760 mm

party_pants said:

normal height of a table is around 760 mm

yes. This one must be one of those you find in pubs and sit around them on stools. which if this is the case is it proper for “little” Amira to be there?

JudgeMental said:

party_pants said:

normal height of a table is around 760 mm

yes. This one must be one of those you find in pubs and sit around them on stools. which if this is the case is it proper for “little” Amira to be there?

Or maybe it’s a standing desk, in which case what do they think they are doing sitting on or under it?

Michael V said:

Michael V said:

1.5 m.

Let:
Amira = A
Barney = B
Table = T

1) A+T-B = 1.3

2) B+T-A = 1.7

Rearrange 1) to solve for T, 2) to solve for B.

1) T = B-A+1.3

2) B = A-T+1.7

Substitute B in equation 1).

T = A-T-A+1.3+1.7
T = -T+3
2T = 3
T=1.5

Or:
Gap 1 = Table height, H, – difference in height, d
Gap 2 = H + d
H = (Gap 1 + Gap 2)/2 = 1.5

Assuming they both sit with exactly the same posture when below or on top of the table.

Barney’s pretty short.

Bubblecar said:

Barney’s pretty short.

:)

The Rev Dodgson said:

Michael V said:

Michael V said:

1.5 m.

Let:
Amira = A
Barney = B
Table = T

1) A+T-B = 1.3

2) B+T-A = 1.7

Rearrange 1) to solve for T, 2) to solve for B.

1) T = B-A+1.3

2) B = A-T+1.7

Substitute B in equation 1).

T = A-T-A+1.3+1.7
T = -T+3
2T = 3
T=1.5

Or:
Gap 1 = Table height, H, – difference in height, d
Gap 2 = H + d
H = (Gap 1 + Gap 2)/2 = 1.5

Assuming they both sit with exactly the same posture when below or on top of the table.

I notice you are adhering to assumptions. ;)

There is something wrong with this thread. No-one has complained about spoilers.

Michael V said:

1.5 m.

Yes, the average of 1.3 and 1.7.

mollwollfumble said:

Michael V said:

1.5 m.

Yes, the average of 1.3 and 1.7.

Show working.

Witty Rejoinder said:

mollwollfumble said:

Michael V said:

1.5 m.

Yes, the average of 1.3 and 1.7.

Show working.

what if it took no effort at all

SCIENCE said:

Witty Rejoinder said:

mollwollfumble said:

Yes, the average of 1.3 and 1.7.

Show working.

what if it took no effort at all

impossible, that would lead to perpetual motion.

Witty Rejoinder said:

mollwollfumble said:

Michael V said:

1.5 m.

Yes, the average of 1.3 and 1.7.

Show working.

I was just thinking that too. Based on the calculations posted earlier. I was wondering if this was just a coincidence with this set of numbers, or if the answer will be the average (mean) between the two figures all the time.

Witty Rejoinder said:

mollwollfumble said:

Michael V said:

1.5 m.

Yes, the average of 1.3 and 1.7.

Show working.

A = table height, B and C are people heights
1.3 = A + B – C
1.7 = A + C – B
1.3 + 1.7 = 2A
so
A = average of 1.3 and 1.7

mollwollfumble said:

Witty Rejoinder said:

mollwollfumble said:

Yes, the average of 1.3 and 1.7.

Show working.

A = table height, B and C are people heights
1.3 = A + B – C
1.7 = A + C – B
1.3 + 1.7 = 2A
so
A = average of 1.3 and 1.7

Or:
Gap 1 = Table height, H, – difference in height, d
Gap 2 = H + d
H = (Gap 1 + Gap 2)/2 = 1.5

The Rev Dodgson said:

mollwollfumble said:

Witty Rejoinder said:

Show working.

A = table height, B and C are people heights
1.3 = A + B – C
1.7 = A + C – B
1.3 + 1.7 = 2A
so
A = average of 1.3 and 1.7

Or:
Gap 1 = Table height, H, – difference in height, d
Gap 2 = H + d
H = (Gap 1 + Gap 2)/2 = 1.5

Yes. I didn’t even need that. I solved it in my head without equations. Each person is added in one equation and subtracted in the other. So the table height has to be the average of the two numbers.

Bogsnorkler said:

Lock in A

Speedy said:

Bogsnorkler said:

Lock in A

+1

What a strange question. The total volume in the milk cup is the same after as before; the total volume in the coffee cup is the same as before. It therefore follows that there is exactly the same amount of milk in the coffee cup as there is coffee in the milk cup.

btm said:

What a strange question. The total volume in the milk cup is the same after as before; the total volume in the coffee cup is the same as before. It therefore follows that there is exactly the same amount of milk in the coffee cup as there is coffee in the milk cup.

Yes, but that’s only obvious once you have looked at it that way.

The most obvious (and incorrect) reasoning is that the spoonful of milk was all milk, but the spoonful of coffee was partly milk, so there must be more milk in the coffee than coffee in the milk.

And I confess to getting it wrong until btm set me straight.

I thought about this question for a few seconds, and decided that life is too short and found something better to do.

captain_spalding said:

I thought about this question for a few seconds, and decided that life is too short and found something better to do.

+1

sibeen said:

captain_spalding said:

I thought about this question for a few seconds, and decided that life is too short and found something better to do.

+1

+1 and also made another cup of black coffee.

The Rev Dodgson said:

btm said:

What a strange question. The total volume in the milk cup is the same after as before; the total volume in the coffee cup is the same as before. It therefore follows that there is exactly the same amount of milk in the coffee cup as there is coffee in the milk cup.

Yes, but that’s only obvious once you have looked at it that way.

The most obvious (and incorrect) reasoning is that the spoonful of milk was all milk, but the spoonful of coffee was partly milk, so there must be more milk in the coffee than coffee in the milk.

And I confess to getting it wrong until btm set me straight.

so no was the correct answer

SCIENCE said:

The Rev Dodgson said:

btm said:

What a strange question. The total volume in the milk cup is the same after as before; the total volume in the coffee cup is the same as before. It therefore follows that there is exactly the same amount of milk in the coffee cup as there is coffee in the milk cup.

Yes, but that’s only obvious once you have looked at it that way.

The most obvious (and incorrect) reasoning is that the spoonful of milk was all milk, but the spoonful of coffee was partly milk, so there must be more milk in the coffee than coffee in the milk.

And I confess to getting it wrong until btm set me straight.

so no was the correct answer

No, yes.

SCIENCE said:

The Rev Dodgson said:

btm said:

What a strange question. The total volume in the milk cup is the same after as before; the total volume in the coffee cup is the same as before. It therefore follows that there is exactly the same amount of milk in the coffee cup as there is coffee in the milk cup.

Yes, but that’s only obvious once you have looked at it that way.

The most obvious (and incorrect) reasoning is that the spoonful of milk was all milk, but the spoonful of coffee was partly milk, so there must be more milk in the coffee than coffee in the milk.

And I confess to getting it wrong until btm set me straight.

so no was the correct answer

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

for the cheap seats int he back.. it doesn’t ask the volume it asks the content… so doesn’t that actually change the answer?

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Yes, but that’s only obvious once you have looked at it that way.

The most obvious (and incorrect) reasoning is that the spoonful of milk was all milk, but the spoonful of coffee was partly milk, so there must be more milk in the coffee than coffee in the milk.

And I confess to getting it wrong until btm set me straight.

so no was the correct answer

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

so no was the correct answer

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

Assume each cup starts with 100mL liquid and a teaspoon has a volume of 1mL.

Conc. Milk (start) = 100%
Volume Milk = 1mL
Final Volume = 100 + 1 = 101mL
Conc. Milk (in coffee) = 1 × 100 / 101 = 0.990099%
Conc. Coffee (w/ milk) = 100 – 0.990099 = 99.009901%
Volume Coffee (w/ milk) = 1mL
Final Volume = 99 + 1 = 100mL
Conc. Coffee (in milk) = 1 × 99.009901 / 100 = 0.990099%

Therefore Conc. Milk (in coffee) = Conc. Coffee (in milk)

The OP is blank for me

dv said:

The OP is blank for me

Because that’s an old one, the new one is further down…

blame the cross domain image linking

It’s okay, I found it in chat.

Should be the same in each.

But just to do the maths…

Initial state:
A: 250 ml milk
B: 250 ml coffee

Intermediate state:
A: 245 ml milk
B: 250 ml coffee 5 ml milk

Return spoon has 5*250/255 = 4.902 ml coffee, 0.098 ml milk

Final state:
A: 245.098 ml milk 4.902 ml coffee
B: 245.098 ml coffee, 4.902 ml milk

dv said:

furious said:

dv said:

JudgeMental said:

The OP is blank for me

Because that’s an old one, the new one is further down…

It’s okay, I found it in chat.

Should be the same in each.

bit as you can see it’s not the same in each post, the OP is different

dv said:

The OP is blank for me

Looks like you’re just too slow.

If you click on “quote” for the OP, then try and follow the link, it goes to a page saying “link expired”

furious said:

dv said:

The OP is blank for me

Because that’s an old one, the new one is further down…

Ah, that explains it!

The Rev Dodgson said:

furious said:

The Rev Dodgson said:

dv said:

The OP is blank for me

Looks like you’re just too slow.

If you click on “quote” for the OP, then try and follow the link, it goes to a page saying “link expired”

Because that’s an old one, the new one is further down…

Ah, that explains it!

and then the subsequent one, for posterity

SCIENCE said:

for posterity

most recent previous

https://twitter.com/ABCscience

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

so no was the correct answer

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

I’m afraid I have no idea what those words in that order mean.

SCIENCE said:

The Rev Dodgson said:

furious said:

Because that’s an old one, the new one is further down…

Ah, that explains it!

and then the subsequent one, for posterity

STEAL?

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

I’m afraid I have no idea what those words in that order mean.

I took it as: show your working…

Witty Rejoinder said:

SCIENCE said:

The Rev Dodgson said:

Ah, that explains it!

and then the subsequent one, for posterity

STEAL?

And one other…

furious said:

Witty Rejoinder said:

SCIENCE said:

and then the subsequent one, for posterity

STEAL?

And one other…

Slate

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Indeed it was.

Although btm’s longer answer was also useful in explaining why it was the correct answer.

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

in no I’m order afraid idea have mean words that I what those

deductive-demonstrative give enough answer correct constructive explanation to fair does feed-forward ‘e the though rather have a than it bit does seem a

roughbarked said:

furious said:

Witty Rejoinder said:

STEAL?

And one other…

Slate

I think the joke in there was ASTLE, as in David Astle, the anagram man.

furious said:

The Rev Dodgson said:

SCIENCE said:

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

I’m afraid I have no idea what those words in that order mean.

I took it as: show your working…

Ah, well how about:

Volume change = coffee added – milk removed
Volume change = 0
Therefore coffee added = milk removed
But all the milk removed was added to the coffee.
Therefore proportion of milk in coffee = proportion of coffee in milk

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

fair enough though it does seem a bit deductive-demonstrative rather than constructive, does ‘e have a feed-forward explanation to give the correct answer

in no I’m order afraid idea have mean words that I what those

deductive-demonstrative give enough answer correct constructive explanation to fair does feed-forward ‘e the though rather have a than it bit does seem a

but in seriousness we mean, looking at the final result and saying “the same amount has to have been exchanged” may be correct (we’ve encountered the puzzle before so that was the solution we recall being given) but it is less convincing to us than an explanation that is worked forward to actually constructively prove that the amount becomes the same

we blame our natural dependence on time and causality for this elitist and superior attitude to looking at mere correlation

Speedy said:

roughbarked said:

furious said:

And one other…

Slate

I think the joke in there was ASTLE, as in David Astle, the anagram man.

https://www.youtube.com/watch?v=dQw4w9WgXcQ

If the answer is STEAL

Then here is the complete list of words that will give 5 yellows

LEAST
LEATS
TALES
TEALS
TESLA

The Rev Dodgson said:

dv said:

furious said:

Assume each cup starts with 100mL liquid and a teaspoon has a volume of 1mL.

Conc. Milk (start) = 100%
Volume Milk = 1mL
Final Volume = 100 + 1 = 101mL
Conc. Milk (in coffee) = 1 × 100 / 101 = 0.990099%
Conc. Coffee (w/ milk) = 100 – 0.990099 = 99.009901%
Volume Coffee (w/ milk) = 1mL
Final Volume = 99 + 1 = 100mL
Conc. Coffee (in milk) = 1 × 99.009901 / 100 = 0.990099%

Therefore Conc. Milk (in coffee) = Conc. Coffee (in milk)

Initial state:
A: 250 ml milk
B: 250 ml coffee

Intermediate state:
A: 245 ml milk
B: 250 ml coffee 5 ml milk

Return spoon has 5*250/255 = 4.902 ml coffee, 0.098 ml milk

Final state:
A: 245.098 ml milk 4.902 ml coffee
B: 245.098 ml coffee, 4.902 ml milk

Ah, well how about:

Volume change = coffee added – milk removed
Volume change = 0
Therefore coffee added = milk removed
But all the milk removed was added to the coffee.
Therefore proportion of milk in coffee = proportion of coffee in milk

yeah we were after more of a furious / dv style solve but we suppose someone with more time than us could do it with variables

dv said:

If the answer is STEAL

Then here is the complete list of words that will give 5 yellows

LEAST
LEATS
TALES
TEALS
TESLA

But the answer is LEAST …
So here is a complete list of words that give 5 yellows…

STEAL
STELA
TAELS
TALES

SCIENCE said:

The Rev Dodgson said:

dv said:

Initial state:
A: 250 ml milk
B: 250 ml coffee

Intermediate state:
A: 245 ml milk
B: 250 ml coffee 5 ml milk

Return spoon has 5*250/255 = 4.902 ml coffee, 0.098 ml milk

Final state:
A: 245.098 ml milk 4.902 ml coffee
B: 245.098 ml coffee, 4.902 ml milk

Ah, well how about:

Volume change = coffee added – milk removed
Volume change = 0
Therefore coffee added = milk removed
But all the milk removed was added to the coffee.
Therefore proportion of milk in coffee = proportion of coffee in milk

yeah we were after more of a furious / dv style solve but we suppose someone with more time than us could do it with variables

Well I did a furiousdv in my head as well, but assumed small cup and large spoon, so

Start:
A: Milk 6 units
B: Coffee 6 units

Middle:
A: Milk 3 units
B: Coffee 6 + Milk 3 units

End:
A: Milk 3+1 units + Coffee 2 units
B: Coffee 6-2 units + Milk 2 units

Are we allowed non-ABC conundrums here?

This is from last week’s New Scientist.

Slightly simplified version:

Anne and Bill are betting on the weather.

Anne bets it will rain for two days, then day 3 will be dry.

Bill says day 1 will be dry, then 2 days rain

They agree that if they are both wrong the bet continues until 3 consecutive days match one of their predictions.

If the chance of rain on any given day is exactly 50/50, who is more likely to win the bet, or do they both have a 50/50 chance?

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Ah, well how about:

Volume change = coffee added – milk removed
Volume change = 0
Therefore coffee added = milk removed
But all the milk removed was added to the coffee.
Therefore proportion of milk in coffee = proportion of coffee in milk

yeah we were after more of a furious / dv style solve but we suppose someone with more time than us could do it with variables

Well I did a furiousdv in my head as well, but assumed small cup and large spoon, so

Start:
A: Milk 6 units
B: Coffee 6 units

Middle:
A: Milk 3 units
B: Coffee 6 + Milk 3 units

End:
A: Milk 3+1 units + Coffee 2 units
B: Coffee 6-2 units + Milk 2 units

all right we’re inspired (and lunching)

A: V, 0
B: 0, V

A: V – T, 0
B: T, V

C: V – T + T / (T+V) * T, V / (T+V) * T
B: T – T / (T+V) * T, V – V / (T+V) * T

T – T / (T+V) * T = T(T+V) / (T+V) – T / (T+V) * T = (T^2 + TV – T^2) / (T+V) = TV / (T+V) = V / (T+V) * T

fine but of course had we been younger and more naive and more bold and daring

we would have used the technique from our peak coding days and considered the following boundary cases

• T = 0 therefore before, middle and after scenarios are identical
• T = V therefore the final result is 0.5 each way which also works
• T in with no further information would also be the same

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

yeah we were after more of a furious / dv style solve but we suppose someone with more time than us could do it with variables

Well I did a furiousdv in my head as well, but assumed small cup and large spoon, so

Start:
A: Milk 6 units
B: Coffee 6 units

Middle:
A: Milk 3 units
B: Coffee 6 + Milk 3 units

End:
A: Milk 3+1 units + Coffee 2 units
B: Coffee 6-2 units + Milk 2 units

all right we’re inspired (and lunching)

A: V, 0
B: 0, V

A: V – T, 0
B: T, V

C: V – T + T / (T+V) * T, V / (T+V) * T
B: T – T / (T+V) * T, V – V / (T+V) * T

T – T / (T+V) * T = T(T+V) / (T+V) – T / (T+V) * T = (T^2 + TV – T^2) / (T+V) = TV / (T+V) = V / (T+V) * T

fine but of course had we been younger and more naive and more bold and daring

we would have used the technique from our peak coding days and considered the following boundary cases

• T = 0 therefore before, middle and after scenarios are identical
• T = V therefore the final result is 0.5 each way which also works
• T in with no further information would also be the same

Which makes me ponder, why did I insist on limiting the size of the spoon to only half a cup, when it is all so much simpler if we assume that spoon volume = cup volume?

The Rev Dodgson said:

Are we allowed non-ABC conundrums here?

This is from last week’s New Scientist.

Slightly simplified version:

Anne and Bill are betting on the weather.

Anne bets it will rain for two days, then day 3 will be dry.

Bill says day 1 will be dry, then 2 days rain

They agree that if they are both wrong the bet continues until 3 consecutive days match one of their predictions.

If the chance of rain on any given day is exactly 50/50, who is more likely to win the bet, or do they both have a 50/50 chance?

I haven’t done a complete analysis yet but I reckon it is Bill. Opportunities for Anne to win really dry up quickly.

dv said:

The Rev Dodgson said:

Are we allowed non-ABC conundrums here?

This is from last week’s New Scientist.

Slightly simplified version:

Anne and Bill are betting on the weather.

Anne bets it will rain for two days, then day 3 will be dry.

Bill says day 1 will be dry, then 2 days rain

They agree that if they are both wrong the bet continues until 3 consecutive days match one of their predictions.

If the chance of rain on any given day is exactly 50/50, who is more likely to win the bet, or do they both have a 50/50 chance?

I haven’t done a complete analysis yet but I reckon it is Bill. Opportunities for Anne to win really dry up quickly.

I think you are right.

Boris said:

Y.

Boris said:

Having given it weighty deliberation, I’m going for M.

Spiny Norman said:

Boris said:

Y.

So is it M or is it why?

The Rev Dodgson said:

Spiny Norman said:

Boris said:

Y.

So is it M or is it why?

An explanation might help us reach a consensus on what the correct answer is.

Witty Rejoinder said:

The Rev Dodgson said:

Spiny Norman said:

Y.

So is it M or is it why?

An explanation might help us reach a consensus on what the correct answer is.

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

The Rev Dodgson said:

Witty Rejoinder said:

The Rev Dodgson said:

So is it M or is it why?

An explanation might help us reach a consensus on what the correct answer is.

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

There are way more planets starting with a Y than I thought there would be:

https://www.bing.com/search?q=planet+names+y&cvid=a80ebd1e5d8540188f2a3307636e4c3d&aqs=edge..69i57j0l8.22608j0j4&FORM=ANAB01&PC=HCTS

but I imagine they would all be too big to be the right answer.

The Rev Dodgson said:

Witty Rejoinder said:

The Rev Dodgson said:

So is it M or is it why?

An explanation might help us reach a consensus on what the correct answer is.

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

Of course, you could make up a sentence using those letters as the start of words and adding another word, and your answer could not be wrong.

buffy said:

The Rev Dodgson said:

Witty Rejoinder said:

An explanation might help us reach a consensus on what the correct answer is.

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

Of course, you could make up a sentence using those letters as the start of words and adding another word, and your answer could not be wrong.

I did think of:
Jesus Said Never Underestimate Evangelical ..

But then I got stuck.

The Rev Dodgson said:

Witty Rejoinder said:

The Rev Dodgson said:

So is it M or is it why?

An explanation might help us reach a consensus on what the correct answer is.

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

M looks to be correct I think.

The Rev Dodgson said:

buffy said:

The Rev Dodgson said:

Well I was just going for a list of planets in order of size, but that’s probably too obvious to be the one true and correct answer.

Of course, you could make up a sentence using those letters as the start of words and adding another word, and your answer could not be wrong.

I did think of:
Jesus Said Never Underestimate Evangelical ..

But then I got stuck.

Varmint

I’ll let you have the honour of adding the noun.

buffy said:

The Rev Dodgson said:

buffy said:

Of course, you could make up a sentence using those letters as the start of words and adding another word, and your answer could not be wrong.

I did think of:
Jesus Said Never Underestimate Evangelical ..

But then I got stuck.

Varmint

I’ll let you have the honour of adding the noun.

Misogyny

So M was right after all.