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Yeah – that is the answer but I’ve always had a problem with it. It assumes that person B is playing with a straight bat. What happens if person B really hates person A and, more that being first to annouce what colour hat they are wearing, they would perfer that person A got it wrong. In that case, it could go like this … person A is wearing a blue hat. Person B looks at A (sees blue), looks at C (sees red), waits until C doesn’t say anything, therefore concludes that they must be wearing red. THEN thinks, now if I pause, then person A will go though the logic you mentioned and annouce RED – oh how sweet that would be when they take off their hat and see blue. So … person B pauses and pauses … and BINGO!

But wait, it gets worse, what if person C really hates person A and B!

is it something like this …

sew becomes stew
Val becomes veal
bead becomes bread
ice becomes rice
Bens becomes beans
hop becomes chop
mat becomes meat

so the secret word is terrace

is it something like this …

sew becomes stew
Val becomes veal
bead becomes bread
ice becomes rice
Bens becomes beans
hop becomes chop
mat becomes meat

so the secret word is terrace

True – but I doubt that they need a lighthouse at the south pole!

Yup – that is correct. I was doing a word puzzle the other day and I thought that I had found south spelt backwards, but instead I had found lighthouse.

ooww – I hadn’t thought of that one – but NO, I don’t think that you can have a star as a land mark. Anyway, my solution also works in the southern hemisphere (without it changing to the southern cross!)

As promised, here is a file that contains three solutions. One based on geometry, one on calculus and one on general principles.

The person who told me about this said that there wasn’t an algebraic solution (for some unknown reason). I didn’t have a pen and paper available, so I assumed that the rower could row at an incredible speed (10x speed of light). With that assumption, the speed of the rower is effectively not affected by the speed of the river, so the rows for 10 minutes down stream and 10 minutes back up stream – a total of 20 minutes. The hat travels 20 x 10 units in that time.

GRRR! One little word that I knew was technically incorrect when I wrote it. It seems I should have made the additional effort to put in SPEED.

Oh – and by the way, you are correct. Care to share how you worked it out?

A man is rowing his boat down stream. At some point, his hat gets knocked off into the water but he keeps rowing. Ten minutes later, he notices that his hat has been knocked into the water, turns around and rows up stream to retrieve it.

The river is flowing 10 units (inches, feet, meters, kilometers take your pick) per minute down stream. Assuming constant speed (edited to remove velocity) and the man has the amazing ability to turn his boat round in 0 seconds, HOW FAR HAS THE HAT TRAVELLED IN THE WATER?

my teacher taught us that the x-axis runs across (a cross = X) the page.

I always remember that.

Here is the answer that I like (already shown above) …

Assuming that there is a solution and given that I’m not given the radius of the sphere, then, the radius of the sphere must be immaterial. Hence, take a sphere of radius 1″ and drill a hole with length 2″ through it. Hence, the resultant cylinder has zero volume and the remaining shape’s volume is the volume of a sphere with radius 1″.

There is a more technical answer in the attachment.

There is also a third way to get the answer that involves integration – I might work on that on the week end and post it next week (if I get really bored).

StuartR – This was the one that I was thinking of.
Tricky – Maybe this only works in America where the drop the h

Ok, a little bit of clarity might help. After you have drilled the hole in the sphere, the resulting solid is 4 inches high – the cut in the sides of the sphere is 4 inches long.

Does that help? If you want the volume of the “cap”, then it is …
v=pi/2 h r^2 + pi/6 h^3 where r is the radius of the bottom of the cap and h is the height of the cap

Wow quick and good work. It does just what I’m after with one tiny draw back – the bars now look too far apart. Is there anyway of having some bars wide and some bars narrow? (And, yes, I know that that is nit picking)

I can always go back to the client and show them one with bars and one without (let them choose).

Thanks a bunch!