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.

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!