puzzles

[Marmalade]

This is a beaut!

Hidden Image/Members Only

hint: do note the clue or get it wrong!!

[contentguy]

Add the digits pointing to the boxes, 12?

Simples

Whats the prob with 7?

[Blackpool Rock]

Well I would say 15 but that last 7 should be an 8 so no doubt 15 is incorrect, too tired to try and work it out now but no doubt it stops me getting to sleep.
Thanks Marm     

Will take a better look tomorrow

[Blackpool Rock]

Add the digits pointing to the boxes, 12?

Simples

Whats the prob with 7?

OK yeah and at least you saved me the trouble 

[Camargue]

Deleted

[Marmalade]

Add the digits pointing to the boxes, 12?

Well that killed it for anyone else!

[timsussex]

Add the digits pointing to the boxes, 12?

Simples

Whats the prob with 7?

spoilsport 


- but why not 21 ?

[Blackpool Rock]

spoilsport 


- but why not 21 ?

Because 2 + 1 + 3 + 6 = 12 not 21 

[timsussex]

this was set in an American SATs paper and EVERY student (out 0f 30,000) got it wrong

Hidden Image/Members Only


unfortunately because the question setter got it wrong and the correct answer isnt ABC or D

Try it with 2 10p pieces - coins of equal sizes so you would expect 1 revolution

[Corus Boy]

Add the digits pointing to the boxes, 12?

Simples

Whats the prob with 7?

The 7 acts to disprove the other potential answer of 15!

Until the 7, you get a working answer by adding two circles in the long chain will give the total of the 'spur' circle.

72 + 27 = 99
27 + 18 = 45
18 + 21 = 39
21 + 15 = 36
15 + 13 = 28
13 +  7  ≠ 21

[Blackpool Rock]

this was set in an American SATs paper and EVERY student (out 0f 30,000) got it wrong

Hidden Image/Members Only


unfortunately because the question setter got it wrong and the correct answer isnt ABC or D

Try it with 2 10p pieces - coins of equal sizes so you would expect 1 revolution

The answer is B (3 times)

[timsussex]

The answer is B (3 times)

Thats what the question setters thought but if you actually try it you dont get 3 - and they had to  renark all 30,000 papers

I dont have a pair of 3 to 1 coins but I do have 2 10ps I would expect the answer for them to be 1 but try it and see what you get

[Blackpool Rock]

Thats what the question setters thought but if you actually try it you dont get 3 - and they had to  renark all 30,000 papers

I dont have a pair of 3 to 1 coins but I do have 2 10ps I would expect the answer for them to be 1 but try it and see what you get

Surely it has to be 

If the radius is 3 times the size then the diameter will also be 3 times the size, pye will be constant for both so cancels out 

If it's not 3 then what is the correct answer 

Trying it at home with 2 x 10p's isn't entirely easy as you will be prone to getting movement / slippage but the circumference of both will be the same so it should logically be 1 

[timsussex]

Surely it has to be 

If the radius is 3 times the size then the diameter will also be 3 times the size, pye will be constant for both so cancels out 

If it's not 3 then what is the correct answer 

Trying it at home with 2 x 10p's isn't entirely easy as you will be prone to getting movement / slippage but the circumference of both will be the same so it should logically be 1 

No its 4!

its easy to do with 2 10p coins where it surely should be 1 but it is 2 !  try it  its not difficult  or you can believe wiki

External Link/Members Only.

There used to be a book called bar bets or something like it filled with puzzles of the move i matchstick variety

[timsussex]

Try this one
Which parts of a Railway Train  are  always moving backwards while the train is moving forwards ?

[Blackpool Rock]

Try this one
Which parts of a Railway Train  are  always moving backwards while the train is moving forwards ?

Passengers facing backwards 

[timsussex]

Passengers facing backwards 

Nope

Its a more difficult variation on this

which 4 parts of a car are usually stationary - even if the car is moving at 70 mph

[Watts.E.Dunn]

Must be a rare event only when ASLEF may permit it;(...

[Blackpool Rock]

No its 4!

its easy to do with 2 10p coins where it surely should be 1 but it is 2 !  try it  its not difficult  or you can believe wiki

External Link/Members Only.

There used to be a book called bar bets or something like it filled with puzzles of the move i matchstick variety

Yeah the Wiki video shows it well but I still had to look a few times and concentrate, it does indeed rotate twice but I still kept focussing on the fact that the original contact points of the 2 coins still met again at the same place and was counting it as 1.

Now i'm not knackered it's obvious that it's down to 1 coin being fixed so having 0 rotations whereas the other one then needs to do twice as many to compensate.
Contrast that to what I was originally imagining with 2 geared cogs of the same size which would then be 1 each

[WASA38]

Yeah the Wiki video shows it well but I still had to look a few times and concentrate, it does indeed rotate twice but I still kept focussing on the fact that the original contact points of the 2 coins still met again at the same place and was counting it as 1.

Now i'm not knackered it's obvious that it's down to 1 coin being fixed so having 0 rotations whereas the other one then needs to do twice as many to compensate.
Contrast that to what I was originally imagining with 2 geared cogs of the same size which would then be 1 each

I find that contrasting of the behaviour of  toothless and toothed circles  fascinating BR. Would the teeth need to be appropriately profiled to ensure smooth meshing since they would effectively be inhibiting the planetary cog from rotating how it naturally should  ? Otherwise might the cogs be liable to jam ? Would it follow that more tooth sliding wear would be incurred with one static cog and one rotating one than would be the case with both cogs rotating ?
 
Anyone here with mechanical engineering aptitude able to enlighten me ?

[timsussex]

I find that contrasting of the behaviour of  toothless and toothed circles  fascinating BR. Would the teeth need to be appropriately profiled to ensure smooth meshing since they would effectively be inhibiting the planetary cog from rotating how it naturally should  ? Otherwise might the cogs be liable to jam ? Would it follow that more tooth sliding wear would be incurred with one static cog and one rotating one than would be the case with both cogs rotating ?
 
Anyone here with mechanical engineering aptitude able to enlighten me ?

the original problem had the larger of the circles fixed in place
Its fairly easy to do with any circular coins with a milled edge place a finger on one coin to keep it in place and with the other hand roll the second coin around it - as I said I saw it in a bar bets book It really is surprising that it makes 2 rotations everybody thinks 1 turn - even the setters of the main USA exam got it wrong I'll bet you a pint 

With regards to toothed cogs then with a bit of lubrication and perfectly fitting teeth well adjusted then wear will be minimal car gearboxes and back axles do several hundred thousand miles and each mile several thousand rotations
Even after many millions of rotations wear can be minimal.

[WASA38]

the original problem had the larger of the circles fixed in place
Its fairly easy to do with any circular coins with a milled edge place a finger on one coin to keep it in place and with the other hand roll the second coin around it - as I said I saw it in a bar bets book It really is surprising that it makes 2 rotations everybody thinks 1 turn - even the setters of the main USA exam got it wrong I'll bet you a pint 

With regards to toothed cogs then with a bit of lubrication and perfectly fitting teeth well adjusted then wear will be minimal car gearboxes and back axles do several hundred thousand miles and each mile several thousand rotations
Even after many millions of rotations wear can be minimal.

Yes, Tim, I having tried this out with two milled coins I can see this now. Although the planetary coin undertakes two revolutions in moving round the static one , only one full circumference of each coin is involved . A corollary is that there would be no difference in wear compared to having two identical cogs intermeshing and rotating about their individual axes.

I really should stop posting things late at night!

[Ahalfa Carling]

Try this one
Which parts of a Railway Train  are  always moving backwards while the train is moving forwards ?

Nope

Its a more difficult variation on this

which 4 parts of a car are usually stationary - even if the car is moving at 70 mph

it is all to do with the wheels:-

In the first question it is the 2nd and 3rd quarters of the wheels (ie the sector from "3'o'clock" to "9'o'clock") that are constantly moving backwards as the wheels rotate.

In the 2nd question it is the tangent where the wheel meets the road (ie the point usually at "6'o'clock) that is stationary and moving neither forwards or backwards (even though that point is constantly changing).

Simples

[timsussex]

it is all to do with the wheels:-

In the first question it is the 2nd and 3rd quarters of the wheels (ie the sector from "3'o'clock" to "9'o'clock") that are constantly moving backwards as the wheels rotate.

In the 2nd question it is the tangent where the wheel meets the road (ie the point usually at "6'o'clock) that is stationary and moving neither forwards or backwards (even though that point is constantly changing).

Simples

Not quite - you are correct about the car - however not the bit about the 2nd and 3rd quarters - no part of a car wheel ever moves backwards while the car moves forwards 

railway wheels similarly the point of contact of a train with the rail is stationary however they also  have a flange  ( to keep them on track )

If you look at a single point on the circumference of  car wheel it moves through a cycloid and is stationary at the point of contact with the road but a point on the flange of a railway wheel (which is a larger circle) describes a different pattern with a small loop at the end where it moves backwards.

The first and third diagram below may help

Hidden Image/Members Only

[Ahalfa Carling]

I shall accept your answer, mainly for the use of the word "Flange"!!

 

[timsussex]

I shall accept your answer, mainly for the use of the word "Flange"!!

 

I do like to make comments appropriate to the site 

[timsussex]

In the spirit of the site heres an old problem dressed to make it a little more appropriate

Tim lives in Worthing which is on the railway line between Chichester and Brighton
He regularly sees 2 WGs  - Hayley in Chichester and Emily Rose in Brighton.

Both offer excellent service and indecisive Tim cannot decide which he prefers so he decides to walk to the Worthing station at a random time and catch the next train in whichever direction it is going West to Chichester or East to Brighton.

There are an equal number of trains in each direction (4 each hour) and all stop so he expected to see each girl an equal number of times but he finds in 8 punts he visits Hayley 6 times and Emily only twice.

Why ?

(As they say on the TV cop shows any resemblance to real people is purely coincidental !)

[Marmalade]

I do like to make comments appropriate to the site 

And you’re clearly into these things Tim! But I’m not sure if I’ve caught up with the last one. Isn’t the answer a bit like a Zeno’s paradox? Even if we show some part of the train is moving backwards or stationary relative to the rest of the train, it’s still moving forward as the whole train is moving forward.

It reminds me of the idea that the Earth moves in an ellipse. While it does so in relation to the sun, it is actually moving in a spiral through space (due to the forward motion of the Milky Way).

[timsussex]

And you’re clearly into these things Tim! But I’m not sure if I’ve caught up with the last one. Isn’t the answer a bit like a Zeno’s paradox? Even if we show some part of the train is moving backwards or stationary relative to the rest of the train, it’s still moving forward as the whole train is moving forward.

It reminds me of the idea that the Earth moves in an ellipse. While it does so in relation to the sun, it is actually moving in a spiral through space (due to the forward motion of the Milky Way).

Not Zeno this time but Aristotles wheel paradox is a bit similar
All motion is relevant and as the earth is rotating and we circle the sun and the milky way is rotating and moving - all at speeds that dwarf our train eg Earth moves at about 67,000 mph around the sun

[Marmalade]

Not Zeno this time but Aristotles wheel paradox is a bit similar
All motion is relevant and as the earth is rotating and we circle the sun and the milky way is rotating and moving - all at speeds that dwarf our train eg Earth moves at about 67,000 mph around the sun

Milky Way rotating? I thought it was moving forward in a logarithmic spiral?

(Though I assume the earth’s spiral will be more regular?)

[JontyR]

Think we should give this a week before we post what we think are the answers?

GCHQ's christmas  puzzles for secondary school kids

Hidden Image/Members Only

[WASA38]

Question 4; answer = TRE , methinks.

Might find time to ponder the others tomorrow but not optimistic. Am no candidate for GCHQ.

[Rick2468]

I saw this one a few years ago and really liked it. I thought it was not possible to solve and was so satisfying when I worked it out.  I can post the solution later if people are interested. I also have another excellent puzzle from the same source that took me a few days to work out which I can share but don't want to flood the thread.

Hidden Image/Members Only

[JontyR]

I saw this one a few years ago and really liked it. I thought it was not possible to solve and was so satisfying when I worked it out.  I can post the solution later if people are interested. I also have another excellent puzzle from the same source that took me a few days to work out which I can share but don't want to flood the thread.

Hidden Image/Members Only

Thanks for this.
I had to resort to the method preferred by constipated mathematicians.

[JontyR]

Question 4; answer = TRE , methinks.

Might find time to ponder the others tomorrow but not optimistic. Am no candidate for GCHQ.

One of us is wrong as I worked out an actual number!

[timsussex]

One of us is wrong as I worked out an actual number!

You could both be correct I also make it TRE - and as each letter is a digit then I could write  .....

[timsussex]

Pretty sure I've got 1 - after all it is a clock puzzle
I have a word for 2 which fits and is ort of linked to 1
3 is easier if you are a Northern Harry Potter football watching stamp collector
I mistyped my earlier answer to 4 missed E off the end - TREE  or in digits it could link to the answers from 1 and 2

[Marmalade]

Question 4; answer = TRE , methinks.

Might find time to ponder the others tomorrow but not optimistic. Am no candidate for GCHQ.

I’ve always hated puzzles, even though I started the thread (I thought that particular one was kind of cute). In fact I don’t mind suggesting them if others like them: but I have a sort of mental block over anyone asking me something they know the answer to (puzzles, basically). So I’m with you on that and won’t try to answer them (Wordle is my limit!).