This time last year, you were no doubt glued to your computer screens each morning to see what lay behind the door on Mrs C's Advent Calender. As we got a bit giddy with all the excitement we've decided to give it a miss and calm ourselves down this year. Instead here's three puzzles for you. First correct answer in the comments box for all three wins er... something good.
1) We are at a Xmas Party exchanging merry banter and you happen to mention that at the last party you attended, it turned out that two of the guests had the same bithday.
Quick as a flash, I offer to bet you £100 that two people in this very room have the same birthday. We quickly count them and see that there are 48 guests. Assume that I have never met any of the guests before; should you accept my bet? (+explain why?)
2) Ignoring your reluctance to engage me in any further conversation, I produce a deck of cards and you notice they all have a number on one side and a letter on the other. I announce that the cards obey a simple rule: if a card has a number three on one side then it must have a letter 'H' on the other.
I throw down four cards onto a convenient table '3' '8' 'T' and 'H'. You have 20 seconds to tell me which of them you need to turn over to prove or disprove my rule.
If you have not timed yourself ruthlessly and submit an answer, I shall know.
3) Even though you are now sidling away from me, I refuse to take the hint and regain your attention by producing a large diamond and three cups. I place the diamond under one of them and shuffle the cups around so that you lose track of where it is. I announce that if you guess correctly then you can keep the diamond. After a brief pause you place your finger on one of the cups. Rather than turning it over, I actually turn over one of the two other cups revealing it to have nothing underneath.
Now I offer you a choice: you can either stick with the cup you have chosen or swap to the other untouched cup. What should you do and why?
The last puzzle is quite famous, so you can have a bonus point if you know its name.