azure
Final Approach
64 is thrown 7 times in all, by pilots 1, 2, 4, 8, 16, 32, and 64. So it's left on.
83 is thrown twice because it's prime, by pilots 1 and 83. So it's left off.
Riddles and Brainteasers
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83 is thrown twice because it's prime, by pilots 1 and 83. So it's left off.
upstateny
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So how many lights are on?
azure
Final Approach
10....
and btw, yes the ones that are on are all perfect squares... and it's because of the interesting property that the divisor function of any number that is not a perfect square is even, but the divisor function of a perfect square is odd.
http://en.wikipedia.org/wiki/Divisor_function
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upstateny
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I took a simpler approach.
The only pilots that will touch any given switch would be the ones that are factors of the number.
Take light 35
Pilots 1 and 35, and 5 and 7 would throw that switch. Since one of the pair would turn it on and the other off, any number with an even number of factors would be off.
But now look at 36
The factors are 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6.
Since the sixth pilot would not throw the switch twice, the light would be on.
As you said, only perfect squares have an odd number of factors and they would be the only ones left on.
The only pilots that will touch any given switch would be the ones that are factors of the number.
Take light 35
Pilots 1 and 35, and 5 and 7 would throw that switch. Since one of the pair would turn it on and the other off, any number with an even number of factors would be off.
But now look at 36
The factors are 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6.
Since the sixth pilot would not throw the switch twice, the light would be on.
As you said, only perfect squares have an odd number of factors and they would be the only ones left on.
azure
Final Approach
Yes, that's the basic reason -- every factor is paired with another factor, except for the case where a number is a perfect square. Then one of the factors is paired with itself so the total number of distinct factors is odd.
I never realized that before either -- so I learned something last night. Always good to be learning!
I never realized that before either -- so I learned something last night. Always good to be learning!
alfadog
Final Approach
Yes, that's the basic reason -- every factor is paired with another factor, except for the case where a number is a perfect square. Then one of the factors is paired with itself so the total number of distinct factors is odd.
I never realized that before either -- so I learned something last night. Always good to be learning!
Would be more tedious to solve if I said there were 37 pilots and 100 lights, no?
Yes, that's the basic reason -- every factor is paired with another factor, except for the case where a number is a perfect square. Then one of the factors is paired with itself so the total number of distinct factors is odd.
I never realized that before either -- so I learned something last night. Always good to be learning!
Excellent
Captain
Final Approach
You're kids birthday party is today. You go to the party supply store in your SUV and pick up a dozen helium balloons. While driving home with the balloons with the windows rolled up a squirle runs out in front of you. You slam on the brakes and screech to a stop.
What do the helium balloons do? Fly to the front of the car? Fly to the back? Stay still?
What do the helium balloons do? Fly to the front of the car? Fly to the back? Stay still?
Fly to the back, crowded out by a horde of eager air rushing forward.
Captain
Final Approach
Correct. Btw, this one was a true story. I stopped suddenly and saw all the balloons crash into the back of the SUV. I figured out why and then played the whole way home doing sudden starts and making the balloons fly up to the front seats and then stopping quick and sending them back. Probably not my safest trip home.
: )
: )
Back, gold fish do the same thing in a Pacer when you seal it up, fill it up, dump 300 gold fish in and go drive around with your buddies in scuba gear with the tires ready to explode.
airguy
Cleared for Takeoff
Back, gold fish do the same thing in a Pacer when you seal it up, fill it up, dump 300 gold fish in and go drive around with your buddies in scuba gear with the tires ready to explode.
bflynn
Final Approach
Captain
Final Approach
Heres one. The answer will be a lat/long near N044 51.727 W093 14.852 (that's near the Mall of America if you're wondering)
The clue is this:
2Big 4Summer 25joy 0zero 24meadow 8before 0naught
8through+12sunshine 10golden 13bright 20water 7joyous 10swarms+7bright 14lake+22trace
I admit up front I don't know the answer to this one. "Hiawatha" may be a clue. With all the brain power on this forum I figure this should be easy.
The clue is this:
2Big 4Summer 25joy 0zero 24meadow 8before 0naught
8through+12sunshine 10golden 13bright 20water 7joyous 10swarms+7bright 14lake+22trace
I admit up front I don't know the answer to this one. "Hiawatha" may be a clue. With all the brain power on this forum I figure this should be easy.
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upstateny
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Ding, Ding, Ding!!!
Captain
Final Approach
What the? Huh? How'd....Where did? I'm lost.
How'd you do that?
PS, happy 1,000th post everybody!!!!!
upstateny
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Hint: Think word count
It's a simple cypher and the poem is the key.
2Big = what word number is Big in the second line = 4
Captain
Final Approach
Geico266
Touchdown! Greaser!
EdFred
Taxi to Parking
A nickel.
Jim Logajan
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I'll buy as many as you have at that price.
Captain
Final Approach
Correct!
audiododd
Filing Flight Plan
Meat!
Meat.
Ahh, beat me lol.
Simple, 2x+1=1.1 2x=.1 x=.05
Captain
Final Approach
Correct.
Sac Arrow
Touchdown! Greaser!
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