Frogger Math [modified]
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Frogger sits twenty feet from a wall. He has just eaten two (slow roasted) flies. ;P Now he sees another fly at the base of the wall! On his first jump, he has the energy to jump half the distance to the wall. (ten feet) :doh: All subsequent jumping power is also cut in half. :(( Question: How many jumps will it take for Frogger to reach the wall? (This is a DISTANCE question, not a "eat the fly" question)
The mind is like a parachute. It doesn’t work unless it’s open.
modified on Tuesday, July 20, 2010 11:33 AM
Richard Blythe wrote:
How many jumps will it take for Frogger to reach the wall
Infinite. He is not going to get to the fly.
The funniest thing about this particular signature is that by the time you realise it doesn't say anything it's too late to stop reading it. My latest tip/trick - Silverlight *.XCP files
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Frogger sits twenty feet from a wall. He has just eaten two (slow roasted) flies. ;P Now he sees another fly at the base of the wall! On his first jump, he has the energy to jump half the distance to the wall. (ten feet) :doh: All subsequent jumping power is also cut in half. :(( Question: How many jumps will it take for Frogger to reach the wall? (This is a DISTANCE question, not a "eat the fly" question)
The mind is like a parachute. It doesn’t work unless it’s open.
modified on Tuesday, July 20, 2010 11:33 AM
Frogger lives in a discrete world, not a contiguous one, so the answer to the question depends on the minimal distance resolution and whether the jump algorithm rounds or truncates.
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3 hops. Because the first jump is 10 feet and the last two are 5. You didn't say it was halved each time. ;-) If you did though, you're talking about an age old math teaser. I believe it was an arrow travels half the remaining distance in a second. How long will it take to arrive at its target? Answer: Never. It will always be some faction of distance away from the target.
Andrew Rissing wrote:
If you did though, you're talking about an age old math teaser. I believe it was an arrow travels half the remaining distance in a second. How long will it take to arrive at its target? Answer: Never. It will always be some faction of distance away from the target.
That's incorrect on multiple fronts. First Zeno created it not to try and disprove motion or anything equally silly but to disprove infinitely divisible time/distance. He failed to do so because the problem he setup requires basic calculus to solve: Specifically Limit N->oo (1-(1/N)), or Sigma N=2 to oo (1/N); both of which are equal to 1.
3x12=36 2x12=24 1x12=12 0x12=18
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Andrew Rissing wrote:
If you did though, you're talking about an age old math teaser. I believe it was an arrow travels half the remaining distance in a second. How long will it take to arrive at its target? Answer: Never. It will always be some faction of distance away from the target.
That's incorrect on multiple fronts. First Zeno created it not to try and disprove motion or anything equally silly but to disprove infinitely divisible time/distance. He failed to do so because the problem he setup requires basic calculus to solve: Specifically Limit N->oo (1-(1/N)), or Sigma N=2 to oo (1/N); both of which are equal to 1.
3x12=36 2x12=24 1x12=12 0x12=18
In the context of when it was presented to me, it was shown as a math problem to say that the arrow would never 'theoretically' reach its target. In the real world, "1 / infinity" is zero, but it was in the context of theory only.