There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, …). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, …). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?
2006-06-15 07:56:20 · 8 answers · asked by Anonymous in Entertainment & Music ➔ Jokes & Riddles
-j is correct.
Bulb 64 is ON at the end (changed 7 times by persons 1, 2, 4, 8, 16, 32, and 64).
The 10 light bulbs that are ON at the end were changed an odd number of times, which are light bulbs 1 (changed 1 time), 4 (3 times), 9 (3 times), 16 (5 times), 25 (3 times), 36 (9 times), 49 (3 times), 64 (7 times), 81 (5 times) and 100 (9 times).
2006-06-15 09:22:39 · answer #1 · answered by pilot612b 2 · 0⤊ 0⤋
Peace is right about part 1...the number 64 bulb is on.
As for Part II, every bulb with a number with an EVEN number of factors will be OFF. Every bulb with a number with an ODD number of factors will be ON. The only numbers with an ODD number of factors are perfect squares. Therefore, the bulbs that will be ON are bulbs 1, 4, 9, 16, 25, 36, 49, 64, 81, 100; that's a total of 10 bulbs left on.
2006-06-15 08:20:55 · answer #2 · answered by -j. 7 · 0⤊ 0⤋
light bulb 64 is on. There are 68 bulbs on. If you want the math, let me know. It's kinda complicated. Pretty much, for the second part you have to write out people one through fifty and then alternate between off and on. Divide one hundred by each person's number to get how many bulbs they either turned off or on. Once you get to the person numbered fifty, then every one else doesn't count because number fifty one will turn one bulb on and number fifty two will turn one off. For all the first fifty, add the bulbs turned on and subtract the bulbs turned off.
2006-06-15 08:29:45 · answer #3 · answered by animal lover 2 · 0⤊ 0⤋
Over 30 years in the past i became asked an identical question in a working laptop or pc flair try regarding a hundred turn/flop switches. by some ability I exceeded, yet even now my recommendations nevertheless hurts. If i assume at No sixty 4, I stand a 50% hazard of having that suited, Being retired now, i'm going to purely savor my brandy and permit youthful human beings warfare with the recommendations detrimental stuff. yet a famous person for the question besides.
2016-12-08 09:26:43 · answer #4 · answered by Anonymous · 0⤊ 0⤋
ok lets see....no 2 switched off 64, number 4 switched it back on, 8 switched it off, 16 switched it on, 32 switched it off, soooo 64 switched it back on!
the other part is beyond my capabilities and I now have a headache
2006-06-15 08:06:02 · answer #5 · answered by 【ツ】ρεαcε! 5 · 0⤊ 0⤋
none, all that switching on and off has burnt out the bulbs.
2006-06-15 08:00:13 · answer #6 · answered by chartneck 3 · 0⤊ 0⤋
complicated task. do a search from yahoo and bing. that can help!
2015-04-05 19:40:50 · answer #7 · answered by ? 2 · 0⤊ 0⤋
Idk... math problems make me cry!
*sob*
2006-06-15 08:00:06 · answer #8 · answered by iamigloo 6 · 0⤊ 0⤋