Any maths teachers on this forum?

The first thing that comes to mind is the gear with the handle and direction indication ISN'T a pinion

Yes, I noticed that but then, as with many of these "gotcha !" type "puzzles" you simple have to try to ignore any pathetic little "gotchas". A bit like "Constantinople is a very big word, but if you can't it, you must be a dunce"

Any joy with the fruit salad on the globe ?

Remember in Latin 'mille' is 1000.

That would be a Milleon then ?  

I don't live in Latin America so don't need that language. 

Err... I think you missed my point I was trying to make about millions, milliards and billions.  Not sure why Americans never took to the Milliard, it is such a lovely word.

MLXVI and all that - I suppose

In the IT storage world, there is a strong trend away from speaking in decimal and towards speaking in binary!

For example, instead of using terabytes (TB) to describe the capacity of a storage subsystem, we are now using tebibytes (TiB).

The prefix "tebi" represents multiplication by 1024.  In the same way 1 terabyte equals1000 gigabytes using decimal, 1 tebibyte = 1024 gibibytes using binary. 

Using binary to describe capacity is more honest, since computers themselves do math in binary. If I tell a technical guy that a system has 300 terabytes of usable capacity, I can tell they are automatically doing the mental arithmetic. It's easier to just state capacity in TiB at about 10% less (300 TB = 272.8 TiB). Instant geek cred!

ATB.

Hook

.....continuing the 1024 instant Geek theme........

GPS time is measured in weeks and seconds from 00:00:00 on 06th January 1980 UTC. An epoch is 1024 weeks, after which the time restarts at zero. GPS time is referenced to UTC but doesn't run in direct sync, so time correlation info is included in the Space Vehicle's broadcast. In July 1999, the difference was about 13 seconds.

So, an epoch has been redefined from some geological tine-scale to a more reasonable and more user-friendly 19 years and 36 weeks (+ or - 13 seconds)

They have to 'Time Dilation' into account!

Ah!

The atomic clocks in the Master and other ground stations provide the reference time and that is what I was refering to above.

As you point out, they also have to take into account that, due to relativity, the atomic clocks in the space vehicles run at a different speed to those in the ground stations and this effect of relativity has to be taken into account in the arrithmetic when calculating reciever positions. 

It's not so much that the clocks run at different speeds, the clocks in fact run at exactly the same speed - it is determined by a very accurate atomic level process.  It's more that time itself runs at a different speed.  Now that is a concept that is difficult for us to grasp. In fact time itself is such an everyday part of our daily lives but can any of us define what time really is?  We could use entropy but not sure that really helps much at all.

I remember that the great Richard Feynman once said when talking about Quantum Mechanics that there is nothing we can relate post Einstein physics to anything in our everyday world (not sure I explained that very well at all).  For example the use of the sun and planets in our Solar System as a model for the nucleus and electrons in an atom does not tell us anything about atomic structure.  Except that electrons are not in the nucleus.

Bloomin' heck, my head is hurting!

I'm fairly sure it is nearly 7 pm in my house. And it still doesn't help us know which Ethernet cable sounds best   

Not the most authorative source, but Wikipedia is sort of readable, even if it isn't particularly accurate...............

Velocity and gravitational time dilation combined-effect tests[edit]

• Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the US Naval Observatory. Two opposite effects came into play. The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40±23 nanoseconds during the eastward trip and should have gained 275±21 nanoseconds during the westward trip. Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59±10 nanoseconds during the eastward trip and gained 273±7 nanoseconds during the westward trip (where the error bars represent standard deviation).^[19] In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment.^[20] The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London–Washington, D.C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity, within the uncertainty of the measurements.
• The Global Positioning System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are corrected for both special and general relativistic time dilation effects as described above, so that (as observed from the earth's surface) they run at the same rate as clocks on the surface of the Earth.^[21]

I don't think it's a trick question, I'd put money on the person who created the image and question doesn't know what a pinion is.

As for the fruit salad on the globe, I gave up on that one after about 10 minutes.

Hope you sleep tight, VladtheImpala.... 

and concentrate on your driving and not the inner workings of your satnav.................

fatcat,

I've put my e-mail address in my profile for half an hour. If you e-mail me, I will send you the "lost" formula for these spheres

I'll try to. I don't mind being a few feet out but I don't want to end up near the France - Belgium border circa 1916.

One to blow your brains out

Cubes, a visual puzzle

Looks like your beaten with the cubes !! Here is an easy one.

Seven.

I might have a go at the the cube puzzle while watching England, especially if it's anything like last Fridays game.

First do this in your head, then   with pen & paper. Did you get it right 1st time ?

.Well I would hazard 4,100 - but I expect it is wildly wrong because I have missed something really stupid.

BB

Once you have done it in your head then get your calculater out and check if you were correct.

No cheating now !!

Mista H

Ok,

Like BB, i'm struggling with this one.

In my head, I said : four lots of 1,000 plus the sum of 40+30+20+10 (which I think is 100), so 4,100".

I then wrote it down on a piece of paper in columns of Th,H,T,U just like I learned at school more than 60 years ago, and .............yes, I got 4,100. So to solve the mystery, I typed them into Excel just as I see them written in "h"'s post and then =Sum() and.............4,100.

Now, I had a cateract operation a few days ago, so I have probably mis-read something that will be bleeding obvious when it's pointed out

So yes, I give up. I just can't see (apologies for the pun, given my recent op) what i'm missing on this one. I await the headmaster's ridicule......

You guys are obviously too clever.

I followed instructions and did it in my head and went from 4090, adding final 10 to say out loud--- 5000.