I direct bridge games and tournaments and create stuff for my bridge work which people seem to want. So I set up this web page to slowly put the things (essays, programs, information) I've created into the public domain. If I were a better writer or programmer I would not be giving them away, but since I am not, I trust you will not descend upon me in anger should they not interest you or work for you...
Nothing on this site has ads or asks for a credit card number (some of the external links might). Since I maintain this site for information and entertainment purposes only, there is no security layer and some browsers may get antsy. I'll do my best to ensure none of these pages is infected with something transmittable so you can safely ignore the warnings that today's browsers insist upon, and we can keep this all free and simple.
Among the things you may currently — or eventually — find here:
(December 16, 2021)
The Twelve Days Of Christmas. You know the song. On the BBC a math professor was asked this question: how many total LEGS in the 12 days of gifts? Answer, remembering that the lower numbered gifts are given multiple times, and that all gifts except the day five golden rings have two legs each, is ... 808. Here's an even more difficult one: in a normal rendition of the song, which verse are you on when you are halfway through?
Not so easy, this, since TTDOC alternates between 4/4 and 3/4 throughout. The opening bit of each verse, "on the nth day of Christmas, etc." is 8 beats, 2 4/4 bars. This is followed by:
Adding up all the beats, we find the first verse ends after 16 beats, the rest after 36, 59, 85, 119, 156, 196, 239, 285, 334, 386, and 441, although in most renditions the final two bars are sung in halved-time so 449 beats in a full, normal rendition. The 225th beat falls in verse eight as we sing about the five golden rings.
Writing is something I do a lot of, editing not so much. If you are prone to the TL:DR* comment, go watch a video on YouTube, the stuff posted here will not interest you. I'd rather read something than watch something and I hate seeing sites switch to video.
* TL:DR stands for 'too long; didn't read.' For someone who struggles to get words and phrases and sentences to fit together, the only comeback to that lazy slam is DILLIGAF, which you'll have to look up on Wikipedia....
That's all for now. I'll put the date of the latest update at the bottom of this page so you can see what's happened.
Last update: October 26, 2024 (at least, the last time I updated and scrolled down to the end to change this line......)