Thursday, September 06, 2007

The Jumping Frog

A frog has fallen into a pit that is 30m deep. (As shown in the colourful illustration by me. X marks the frog!)


Each day the frog climbs 3m, but falls 2m at night. How many days does it take for him to escape?


I invite your answers to this 'problem', if you want to call it that. It was given to me by MH, and once again I was mocked. :( They expect too much of me, people do. I mean just because I like maths, doesn't mean that I should be able to answer problems like the one above, straight away! The fact that MH and another person had solved it put the pressure on me. I bought some time by claiming to be busy, and it worked.

I don't know if the answer I have is right, but I'm sure if someone posts their solution I can always confirm if I got the same! (For those who want proof that I have some answer, I have taken a picture of it. Once I get confirmation in the morning, I will let you know. :D)

Oh, and no guessing random numbers; a small explanation would be nice (if indeed you do bother having a go)! My first 'guess' had been: 'All the numbers from 1 to n, where n=30'. This took a while to register (haha), but I was given a stern look in return. Have fun.

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PS: I did some maths toady! It's true; I looked over permutations because we had done quite a few proofs by 'strong induction' in the notes, and I had found it fuzzy. It still does seem like mumbo jumbo, what with this max(s,t) business. It know it's (sort of) obvious, but is there a way of getting from max(s-1, t-1) to max(s, t)-1? If s does not equal t, then max(s-1, t-1) is defined to be either s-1 or t-1, whichever is greater (not taking into consideration that s might equal t). In the same way, max(s, t) can either be s or t (whichever is greatest). Subtracting one from max(s,t) gives me what I want, but it all seems rather 'dodgy'. Hmm, I better dig up the book I have on reasoning...

Another 'oh', but when doing proofs I would first advise(?) you to plug some numbers in, to see what is happening. Well, it's not necessary and not possible for some proofs, but give it a try when trying to prove that there are infinitely many primes (and other such proofs). It might aid you in remembering proofs, or remembering how to go about proving them.

3 comments:

beans said...

I got the answer confirmed for me in the morning, and you can find it here. I did feel a certain degree of satisfaction as well; not because I got it right, but because MH zipped his mouth for once!

KTC said...

Hehehe, yes that's the right answer, because on day X (where X is the answer), something special happen that doesn't happen on day 1 to X-1.

beans said...

*high five* :p

That something special is so special that I overlooked it on first glance. (Poor Freddo the frog.) However, I have to admit that the question was quite sly!