Food for thought...

A crazy (suspected Brit?) explorer wishes to cross a desert on foot. It takes six days to cross the desert. One man can carry enough food for only 4 days. Under this scenario, using trial and error, you can find the fewest number of men required so that the explorer crosses the desert and the coolie(s) return(s) alive. What is this minimum number? (0.1 point - sorry, this is easy!)

The real question (1.0 point) is to find an elegant logic to generalize this problem. That is, if it takes N days for an explorer to cross the desert and each man can carry enough food for k days, what algorithm should be employed to attain the objective?

Does it ring a bell?

Can a wind chime be viewed from an angle so that the tips of the chime rods fall in a single plane? (Non-trivial solutions only allowed)

Even-steven

Twelve iron canon balls have the same weight, but for one that has a different weight. Find the odd ball, using only three weighings on a balance scale and determine whether it is light or heavy.

Vowel talk...

Find three English words that have the vowels a,e,i,o and u in order.

0.2 points for each word upto a maximum of 1.0. No googling allowed.

The attack of the academics...

Here is a rather academic problem which nevertheless reduces to some other interesting problems:

What is the expected value of the maximum of N random variables, each of which is between 0 and 1?

What is the expected maximum value of 2 variables under the constraint x+y=1?

If you have figured each of these out, you have passed the qualifying round for this month's IBM ponder this!