IBM Research | Ponder This | January 2012 challenges

# Ponder This

## January 2012

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Ponder This Challenge:

This months challenge is based on an idea from Anees Shaikh.
For each natural number there is a lamp.
At the beginning (Midnight between Saturday and Sunday), all the lamps are off.
1/2 of a second later came a little dwarf who switched their state (i.e., turned them all on).
1/4 of a second later, another dwarf comes and toggles the lamp switch for every second number. Now all the even lamps are off again and all the odd ones stay on.
1/8 of a second later comes yet another dwarf and toggles the lamp of every third number: the number 3, which was on, gets turned off, the number 6 which was off is now on, etc.
1/16 of a second later, another dwarf toggles every fourth number, and so on (after 1/2^n of a second the dwarf toggles all the numbers that are divisible by n).

Meanwhile, a red dragon is learning to count:
It counts "one" and drops a flammable egg near lamp #1.
It counts "one, two" and leaves another egg near lamp #3.
It counts "one, two, three" and places an egg near lamp #6.
It counts "one, two, three, four" and lays an egg near lamp #10; and so on.

The red dragon walks at a constant pace of one lamp per second.
Suddenly, he lays an egg too close to one of the lamps, which was on at the time, and therefore hot, and it immediately explodes.
The explosion ruined the lamp's number sign, but the last three digits are still visible: "576".
When did the explosion occur? What day of the week, hour, minutes, and seconds?

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 01/01/2012 @ 10:00 AM EST
Solution: 02/01/2012 @ 10:00 AM EST
List Updated: 01/01/2012 @ 10:00 AM EST

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