Zoo Station

I just got back from India, and had the chance to look at Mindsport again. Mukul Sharma still runs an interesting column and, for those who have never seen it before, Mindsport is worth a look. I would like to, however, warn readers of Sharma's surprising political incorrectness. In a column a few weeks back, he went so far as to ask readers to 'go jump into the nearest well' (and I am quoting from memory here), if they couldn't solve a particular puzzle. Sharma has a tendency to rant, gloat and criticize. This can get pretty annoying for readers, confusing for young researchers and even demotivating. To put the puzzles in perspective, they are merely one way of measuring analytical ability. An ability to do well at solving these puzzles is not in itself anything more than one indicator of intelligence. High scores in such tests are not a guarantor of research ability but, of course, have a positive correlation. Amit, who has been to the International Mathematical Olympiad and is also involved in highly mathematical Computer Science research, might have more to say on this.

Here is this week's endgame and the solution.

ENDGAME

There is a prison with 365 cells. Each cell has a lock which alternately opens and closes with the press of a single button on its gate. The jailer, for some weird fancy, starts his morning rounds on 1st January 2003 and presses all the buttons opening all the cells. On the next day, he presses the buttons on all cells which are multiples of two, closing them. Day three, and he does that to multiples of three, then four, and so on and so forth, till the end of the year when he presses the button on cell 365. Question: Which cell numbers are open and which closed on 1st January 2004?

(Submitted by Pankaj Sharma MD, indiapankaj@sify.com)

The solution and the rest of the post is out here.