P-007 A powerful paradox!

Consider an infinite tower of powers of x:

Y = x^(x^(x^(x …

‘^’ is the exponentiation operator.

The equation Y = 2 can be solved by noting that Y = x^Y, so that 2 = x^2, or x = sqrt(2).

But then, if Y = 4, we can similarly solve for 4 = x^4, giving 2 = x^2 again. So the question is, what is the value of Y when x = sqrt(2)?

In general, what is Y(x)?

P-006 Another multicore cable puzzle

There is a long n-way multicore cable and you have to match up the wires on the two ends, making a minimum number of trips from one end of the cable to the other. The only tool you have is a continuity tester. You can connect the wires on either end in any  combination.

There are several strategies that I know of but they are all equally good in terms of number of trips needed.