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Going the rounds at school a long time ago were the following, which I have never encountered anywhere since:--
"Why is a mouse when it,s spinning ?" and
"If a hen and a half lays an egg and a half in a day and a half, how long will it take six hens to lay six eggs ?"
We were led to understand that there was a logical explanation of the first, and a formula to answer the second . Can anyone put me out of my misery after all these years ?

Correction. The first should read "Why is a mouse when it,s spinning ?" and the answer was said to be " Because the higher the fewer," and there is supposed to be a rational explanation !

Correction. The first should read "Why is a mouse when it,s spinning ?" and the answer was said to be " Because the higher the fewer," and there is supposed to be a rational explanation !

If the question was "How high is a mouse when it's spinning?" (How high sounds like why) then in conjunction with the following from Google the answer "The higher the fewer." almost makes sense.

And the meaning had to do with the centrifugal governor on an old steam engine - the weight was called the mouse, and as the engine rpm increased the mouse would rise due to centrifugal force. But as the mouse rose, the arm would force the steam valve in the more closed direction, thus reducing the rpm, that is, the higher (the mouse), the fewer (rpms).

Years at KBGS e.g. 1958-1964 (optional) 1954-59

Current location (optional) Denholme (garethwhittaker99@hotmail.com)

Quite right Gareth. Somehow, I remember Peter posing the same 'conundrum' some 2/3 years ago, and my brother Arthur posting the very same answer, almost verbatim, so I can only assume he picked it up off Google himself.
Just to keep your 'grey matter' active, try this one:-
'A fox completes the same round trip every evening. If he covers his outward journey at 175 meters/hour, and returns over exactly the same distance at 70 meters/hour, what is his average speed for the entire journey? Blow the dust off those old Algebra books!!

I work it out to be 144, but then again, I do have an IQ in excess of 120.

Reasoning
2+3=10
2+3=5 (x 2 ie the 1st number of the pair)=10
7+2=63
7+2=9 (x 7 ie the 1st number of the pair)=63
6+5=66
6+5=11 (x 6 ie the 1st number of the pair)=66
8+4=96
8+4=12 (x 8 ie the 1st number of the pair)=96

Beaky would have been proud of me, probably not. I still don't know what a Brownhenway is though.

Years at KBGS e.g. 1958-1964 (optional) 1958-61

Current location (optional) Blue Mountains, Australia via Haworth

Thank you ,David, for reminding me of Arthur´s explanation of a couple of years ago. As I read Gareth´s response I realised I had heard it before------it must be the tequila !

Terry your maths problem is neat. Ever the pedant especially in things mathematics which prides itself in precision of language I have to insist that in a way the question is unfair, or rather incorrectly posed. The use of conventional notation + (plus) and = (equals) is misleading and of course deliberately so to fog the solution. What we are required to really do is define the function that maps a given pair ( x, y) to a single element(z).
I am not sure of the correct functional notation but it probably will look something like this:
If f ( x, y) -> z
And given that f(2,3) -> 10 and f (4,5) ->36 etc ……… define f

The answer being that for any pair ( x,y) the function f maps the pair(x,y) to z where z = x( x+y)

I can remember the time when giving an answer without an explanation as to how you had arrived at it would have got you a clip round the lug'ole. It may well be right(it might also be a wild guess!)

I'd better steer clear o' thee - or at least not tek mi lug'oles wi' me.
OK.
You need at least 50% probability of 2 people with the same b'day - so less than 50% probability of all having different b'days.
First person certainly has a birth date - prob 100%.
Second person has a different birth date - prob (364/365 x 100)% = 99.7% approx.
Third person has a birth date different from both these - prob (363/365 x 364/365 x 100)% = 99.2% approx.
Etc. etc.
When you get to the 23rd person this equals slightly less than 50%. Q.E.D.

Can you find integers x, y and z such that x cubed plus y cubed = z cubed, or can you show that this can't be done. First correct answer gets a pint of Landlord.