Answer: Christmas Teasers
1. This is a tricky puzzle and admittedly the answer involves a somewhat unlikely scenario. The only way I can celebrate my birthday two days before Nicolette is if she was born east of the International Date Line on March 1st of a non-leap year. Assuming we’re travelling (for example, on a flight or a boat), I could then be born nine minutes later west of the International Date Line where it would be February 28th. If this was the case, on any subsequent leap year, I would celebrate my birthday two days before Nicolette.
2. We’re told that:
The limit as n -> ∞ of x^x^x^x^x… (n terms) is equal to 2.
Therefore, the limit as n -> ∞ of x^ [x^x^x^x… (n terms)] is equal to 2. So x^2 = 2. And hence:
x = √ 2
Here’s a crude numerical approximation courtesy of the brilliant Wolfram Alpha that illustrates the answer.
