Puzzles

[new_trader]

Wait now, let me double check this.

If 1.5 duck lays 1.5 eggs in 1.5 days - then how can 1 duck lay 1 egg in 1.5 days.

Should it not be - 1 duck lays 1 egg in 1 day, or .75 duck lays 0.75 eggs in 0.75 days?

Not by by calculations.

1 duck lays twice as fast as 0.5 ducks and they both start laying at the same time. If in 1.5 days there are 1.5 eggs then 1 duck has done twice as much work as 0.5 ducks. A ratio of 2:1 means 1.5eggs/3 = 0.5.

1 duck = 2 x 0.5 = 1 egg
0.5 duck = 1 x 0.5 = 0.5 egg

 

[CYOF]

Hmmmm...If the answer is 24 as you suggest, then 1 duck lays 4 eggs in 6 days. Which means 1 duck lays 1 egg every 1.5 days....

Ok, let me see.

If 1.5 duck lays 1.5 eggs in 1.5 days...........then............subtracting a third..............we get 1 duck lays 1 egg in 1 day.

So, this would mean that 1 duck would lay 4 eggs in 4 days - not 6 eggs?

 

[new_trader]

Ok, let me see.

If 1.5 duck lays 1.5 eggs in 1.5 days...........then............subtracting a third..............we get 1 duck lays 1 egg in 1 day.

So, this would mean that 1 duck would lay 4 eggs in 4 days - not 6 eggs?

Are you winding me up

Is the answer 24 eggs or not?

If 1 duck lays 1 egg every day then 6 ducks lay 36 eggs in 6 days...

What is the answer...24 or 36??

 

[firewalker99]

Correct - but I hope this was not a guess - guessing is not allowed

Maybe when one gets a question right they can post their solution once the answer is confirmed - what do you all think ?

No not a guess I didn't want to post the solution straight away for not spoiling the fun for others. But perhaps we can all learn from different solutions (and different ways of thinking!)

So this is how I see it:

1.5 duck -> lays 1.5 eggs -> in 1.5 days

first we multiply the number of ducks
6 ducks (1.5x4) - lay 1.5 x 4 = 6 eggs -> in 1.5 days

then we multiply the number of days
in 6.days (1.5x4) <- we have 24 eggs <- from as many ducks 6 (this doesn't change)

It's a typical example of how most people would answer straight away "6"...

 

[CYOF]

Are you winding me up

Is the answer 24 eggs or not?

If 1 duck lays 1 egg every day then 6 ducks lay 36 eggs in 6 days...

What is the answer...24 or 36??

Yes - the answer is 24.

Let me check FW's post to see if it makes sense.

 

[firewalker99]

Ok, let me see.

If 1.5 duck lays 1.5 eggs in 1.5 days...........then............subtracting a third..............we get 1 duck lays 1 egg in 1 day.

So, this would mean that 1 duck would lay 4 eggs in 4 days - not 6 eggs?

No, 1 duck doesn't lay 1 egg in 1 day that's not correct:
adding or subtracting changes the proportions which makes the computation incorrect, that's why we need to multiply (or divide)

1.5 duck lays 1.5 egg in 1.5 day --> divide this (but only the right part!) by 1.5 to get the days
==> in 1 day we have 1 egg from 1.5 duck

if we only have 1 duck we need to divide by 1.5 once more
==> in 1 day we have 1/1.5 (=0,66... ) from 1 duck

 

[new_trader]

Yes - the answer is 24.

Let me check FW's post to see if it makes sense.

If mine doesn't make sense then all maths textbooks would need to be rewritten, surely?

 

[CYOF]

No not a guess I didn't want to post the solution straight away for not spoiling the fun for others. But perhaps we can all learn from different solutions (and different ways of thinking!)

So this is how I see it:

1.5 duck -> lays 1.5 eggs -> in 1.5 days

first we multiply the number of ducks
6 ducks (1.5x4) - lay 1.5 x 4 = 6 eggs -> in 1.5 days

then we multiply the number of days
in 6.days (1.5x4) <- we have 24 eggs <- from as many ducks 6 (this doesn't change)

It's a typical example of how most people would answer straight away "6"...

first we multiply the number of ducks
6 ducks (1.5x4) - lay 1.5 x 4 = 6 eggs -> in 1.5 days

If 6 ducks lay 6 eggs in 1.5 days - then 6 days is 4 times greater than 1.5 days - so we multiply 4 x 6 = 24

Another solution:

First, double the time = 1.5 ducks lay 3 eggs in 3 days

So = 1.5 ducks lay 6 eggs in 6 days - just double again

So = 6 ducks, been 4 times greater than 1.5 ducks, will lay 4 times as much

Or = 6x4 = 24 = 6 ducks will lay 24 eggs in 6 days

 

[new_trader]

first we multiply the number of ducks
6 ducks (1.5x4) - lay 1.5 x 4 = 6 eggs -> in 1.5 days

So now, you agree with me? :cheesy:

If 6 ducks lay 6 eggs in 1.5 days it means that 1 duck lays 1 egg in....yep, you guessed it, 1.5 days

 

[CYOF]

No, 1 duck doesn't lay 1 egg in 1 day that's not correct:
adding or subtracting changes the proportions which makes the computation incorrect, that's why we need to multiply (or divide)

1.5 duck lays 1.5 egg in 1.5 day --> divide this (but only the right part!) by 1.5 to get the days
==> in 1 day we have 1 egg from 1.5 duck

if we only have 1 duck we need to divide by 1.5 once more
==> in 1 day we have 1/1.5 (=0,66... ) from 1 duck

Very good point FW, I was actually after forgetting all about the proportion change when adding or subtracting - makes you think how much simple things you really forget over the years.

 

[CYOF]

So now, you agree with me? :cheesy:

If 6 ducks lay 6 eggs in 1.5 days it means that 1 duck lays 1 egg in....yep, you guessed it, 1.5 days

I stand corrected - but you were doubting were you not - and is it not also good to know when you are right, even though others may lead you to think that you may be wrong - another valuable lesson of course.

Good show.

 

[firewalker99]

Very good point FW, I was actually after forgetting all about the proportion change when adding or subtracting - makes you think how much simple things you really forget over the years.

You'd be amazed at how much stuff we learned over the years but are forgotten or hidden in the back of our heads somewhere... These puzzles are refreshing and a brain teaser a day keeps dementia away :cheesy:

 

[new_trader]

I stand corrected - but you were doubting were you not - and is it not also good to know when you are right, even though others may lead you to think that you may be wrong - another valuable lesson of course.

Good show.

I never doubted my solution because as someone always used to say to me: "Maths never lies"

How you going with the 12 ball thing?

Does anybody want some hints?

 

[barjon]

weigh in lots of 3,nt?

 

[new_trader]

weigh in lots of 3,nt?

No. Hint (below)
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1) Divide the balls into 3 groups

Group A - 1,2,3,4
Group B - 5,6,7,8
Group C - 9,10,11,12

2) 1st Weighing

Group A on Left, Group B on Right, Group C Aside
If scale tips Left or Right then all Group C balls are OK
If scale tips Left then Group A has an ODD Heavy Ball or Group B has an ODD light ball
If scale Balances then Group C contains the ODD ball

If Scale Balanced on 1st weighing:

Then for 2nd weighing

1,2,3 on left and 9,10,11 on right, 12 left aside

 

[CYOF]

Ok, I will leave you with this one, as I must go and do some work!

Riddle:

With each letter representing one number, identify the correct numbers in the subtraction problem.

ZBZ
-CZ
-------
ZB


Or ZBZ-CZ = ZB

I have not tried this yet.... I will later....but I do have the answer to look up.

 

[blackcab]

I just did the duck one and got it in half a minute (without reading the followup posts).

d = ducks, t = time (days), e = eggs

1.5e = 1.5d * 1.5t

:. e = (1.5d * 1.5t) / 1.5

Substituting 6:

e = (6d * 6t) / 1.5

= 36 / 1.5

=24

I think with these puzzles the key is in framing the question in the right way. With the John, Jim, Joe one it was easy to get straightaway by writing their names in a vertical column, putting them where the question said they were in relation to each other - the answer comes out immediately that way.

The Einstein riddle looks like one of those three dimensional logic puzzles, but with five dimensions. Eee, I'm never going to get any work done today!

 

[CYOF]

I just did the duck one and got it in half a minute (without reading the followup posts).

d = ducks, t = time (days), e = eggs

1.5e = 1.5d * 1.5t

:. e = (1.5d * 1.5t) / 1.5

Substituting 6:

e = (6d * 6t) / 1.5

= 36 / 1.5

=24

I think with these puzzles the key is in framing the question in the right way. With the John, Jim, Joe one it was easy to get straightaway by writing their names in a vertical column, putting them where the question said they were in relation to each other - the answer comes out immediately that way.

The Einstein riddle looks like one of those three dimensional logic puzzles, but with five dimensions. Eee, I'm never going to get any work done today!

I must say, I like your approach bc, must look into this more!

I will be keen to see your workout for the 5 houses, etc, as I got caught with the Dane and the Brit -and only worked it out with trial and error - it took me nearly 2 hrs.

Would like to see if this can be done quickly by using a layout or matrix of some sort - as in 10 min or so.

 

[blackcab]

With each letter representing one number, identify the correct numbers in the subtraction problem.

ZBZ
-CZ
-------
ZB

Z=1
B=0
C=9

Right-hand column: B is Z-Z, so is B=0.

Middle column: add 10 to B in top row in the standard subtraction way, so Z=10-C

Left column: Add 1 to bottom row in standard subtraction way. There's no hundreds digit in the bottom row, so Z-1=0, so Z=1. Therefore if Z=10-C, C=10-Z = 9

 

[SOCRATES]

......Thought I would give you a bit of help...

the ducks...

Answer= 36

The Einstein problem= The German has the fish, he drinks water, smokes Prince and lives in the last house on the extreme right, painted white.

And the zb riddle...

the top figure is 101
the middle figure is 91
and the bottom figure is 10

The balls riddle :

Take only 8 balls out of the 12...thus splitting them into two groups of 8 and 4.

you may be lucky and the 4 balls are of the same weight...but in any event...split the 8 into two groups and weigh 4 against 4....if the balance is even, the odd ball is in the group of 4.

now proceed as follows;~

weigh the first group of eight (4 against 4 ) to see if they balance...if they do...then the odd ball is in the other group of 4...if not...it is in the group of 8.

take the heavier side, split into 2 and 2....balance them...see which two are heavier...then...take the two on the heavier side and balance them one against the other...thus the heavier ball can be detected.

...going back to the hens and the eggs:~

the calculation is as follows:

1.5 divided by 1.5....= 1...multiplied by 6...=6...multiplied by 6 = the answer = 36.

...a doddle really...:cheesy: