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Pastimes : Where the GIT's are going -- Ignore unavailable to you. Want to Upgrade?

To: ManyMoose who wrote (189275)	1/2/2010 4:48:39 PM
From: Glenn Petersen	Read Replies (2) \| Respond to of 225578

Happy Palindrome Day! Monday Puzzle: Backdating By PRADEEP MUTALIK New York Times December 28, 2009, 8:36 am Justin Thyme The upcoming New Year’s Day is special since it starts a new decade, but as this “date odometer” shows, the next day has an even rarer numeric property. _______________ The year-end holidays are here - ’tis the season of parties and hangovers! I trust all of you are enjoying the holiday festivities and partying hard. This week we have one more reason to eat, drink, sing, dance and be merry: New Year’s Day 2010, the end of the first decade of the 2000s. Celebrating the new year is a time-honored tradition, but if you think about it, it’s nothing more than a celebration of a numerical event, when the odometer of time turns up one or more new digits. For the party-animals we humans are (Homo partiens) that’s reason enough. So go ahead and party. Uncork the bubbly at midnight and kiss your special one at the moment the ball drops. But don’t party so hard that you can’t do it again in a couple of days. You see, something numerically rare and special is going to happen on the second day of the New Year, which falls conveniently on a Saturday. That day is a palindromic date in standard American (mmddyyyy) format: 01-02-2010, expressed backwards as a date is precisely 01-02-2010.* It’s something rare—rarer than a decade change, even—and deserves a bigger party! Nice time to talk about déjà vu and time going backwards… How rare is this event? Let’s find out. 1. First a warm-up question. When was the last palindromic date (before the one coming up on 01-02-2010) in mmddyyyy format? How about the one before that? 2. How many palindromic dates are there in mmddyyyy format between the dates 01-01-1000 and 12-31-2999 inclusive? Suppose that the rarity of a date dictates the size and intensity of the party it deserves. Now the standard measure of the size and intensity of a party is the “hangover stars” scale which is based on the numbers of stars you see when you wake up the next morning. The hangover scale goes as follows: an otherwise unremarkable new year deserves a party that gives only a 1-star hangover; a decade change deserves a 2-star party because it is rarer; a century change, 3 stars; and a millennium change, 4 stars. 3. Based on the answer to question two and the rules followed by the above scale, how many hangover stars does a party to celebrate a palindromic date deserve, to two decimal places? 4. When will January 02 again be a palindromic date after the year 2010? We were alerted to the impending palindromic day this week by Dr. Aziz Inan, Professor of Electrical Engineering at University of Portland in Portland, Oregon. Dr. Inan loves making up math puzzles and is currently working on a recreational book of math puzzles. He has done a thorough analysis of palindromic dates in different formats and has devised some of today’s problems. As Dr. Inan remarks, it seems as though he was born to make up puzzles, because if you take his first name (AZIZ), swap the odd letters and rotate the even ones 90 degrees, you obtain his last name (INAN)! Our readers have already been having fun with palindromes as word challenges this past week, so let’s continue to do so. How about some palindromic sentences on the themes in this puzzle like parties, special dates, New Year’s Day, and palindromes themselves? Also do you know of any people with palindromic or quasi-palindromic names like Dr. Inan? Since there wasn’t a formal word challenge last week, I’ve posted another palindrome-based word challenge in the comments on last week’s puzzle here. As usual, you can submit answers as comments here. Comments posted today will not be released for a day or two. We’ll award a copy of Martin Gardner’s book, “My Best Mathematical and Logic Puzzles,” to someone who comes up with an especially interesting answer to today’s puzzles or to someone who proposes a sufficiently intriguing puzzle for Lab readers to solve. A copy of that book is being awarded to Dr. Aziz Inan for his suggested puzzles. Thank you, Dr. Inan! We hope to use some more of your puzzles in future columns. (To submit a new puzzle, send an e-mail message with “NEW LAB PUZZLE” in the subject line to tierneylab@nytimes.com. Please include the solution to the puzzle and indicate whether or not the puzzle is original.) Happy New Year and Happy Palindrome Day to all. Have fun, and if you find yourself seeing everything backwards, or worse —if you find yourself “backdating” your ex—you’ll know ’tis the time to stop. ———– Corrected Tuesday December 29 2009, 8:30 am: I had originally said “first decade of the third millennium” which as many readers pointed out, is wrong. Copyright 2010 The New York Times Company Comments can be found here at the bottom of the article* tierneylab.blogs.nytimes.com