Tuesday, October 6, 2009


A light rain like trickle of little droplets of water, sounding a little like rain drops falling on clay pots. Then a rush of water, a wave of smooth water traveling over its wavy surface. A soft calm stroking in the sound and presence of quick water. Waves in the background, so soft that it calms the spirit. A quick few hard strokes along the water’s welcoming presence. The innocent soul then leaves the water and the rushing waves continue on. A sudden plunge enters the soft water and a swishing sound soon follows the deep plunge. Lastly a few small droplets drop into the water finishing the moment.

http://margaretnoble.net/blog/monte-gordo-beach-portugal/comment-page-1/#comment-153

Thursday, October 1, 2009

1000 lockers

There are 1000 lockers and 1000 students oped the lockers. The first student opens all the lockers. The second student changes the position every second locker starting on the second locker. Next the third student changes the position of every third locker starting on the third locker. Then the fourth student and fourth locker and the pattern continues. The question is which lockers are left open? The answer is 31 lockers are left open. This is the right answer because there are 31 perfect squares including the very first locker. The perfect squares involve; 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961. This is all 31 perfect squares. To get 1000 you would need to add on decimals to 31. Approximately another 30 or so digits in the decimal places. The answer is 31 because the locker number is accessed as many times as it has divisors. Ex: Locker number 6 is accessed 4 times - by the first, second, third and sixth kids. Thus the lockers which will be open are those whose number has an odd number of divisors, i.e., perfect squares. The number of perfect squares less than 1000 is 31.