Solutions to riddles

Yes, of course it does. It only takes 104 hours. Since the books in a bookshelf is standing with their backs out, the word "A" in the first volume is to the far right, while the word "Zzzax" in the last volume is to the far left, thus it only needs to eat 6000 pages plus 4 covers.

Well done Marius, no need for hint.

Now try the prisoners one... (hint tomorrow ?)

I've already solved the prisoner one (together with others, I admit), so I will leave it up to others to post the solution to that one... :-)

Easy one: Not sure exactly what you mean by "normalized", but I expect that you mean that the number before x^99 is 1. Then the polynomial has to be (x-1)*(x-2)*...*(x-99). The values for x=0 and x=100 is then 99! (99 faculty = 99*98*...*2*1).

Nop, try degre 3

Nearly... when you find it, what about original one I spoiled:

P(x)=x for x=1..99, normalized again (yes you are right, any name for that ?).

P(0)=?

P(99)=?

I meant f(0)-99!, ofcourse (forgot the minus sign). f(100)=99!. Is your new puzzle so that f(x)=x for x=1,2,...,99? And we still are supposed to find f(0) and f(100)? I suppose the polynomial (x-1)*(x-2)*...*(x-99)+x should take care of that one (if I understood your puzzle correctly). Then f(0)=-99!, and f(100)=99!+100.

As for the difficult one, I have found two numbers with the mentioned property, but I have not yet managed to prove that they are the only two numbers with that property...

Well done again.

For the difficult, I have the start of a proof but I ended up trying all 10 digits numbers, keep on, a lot can be said.

I will be interested by your progression.

Snail and elastic riddle:

The snail will be moving a little faster than 1 cm/hr because the stretching elastic is pulling it along. Even if the snail did not move, the percentage of the journey completed would not be affected by the stretch so the snail is making progress by crawling forward. As the elastic gets longer, crawling 1 cm will complete 1/100th of the journey in the first hour, 1/200 in the second hour, 1/300 in the third.... This is just 1/100 times the harmonic series. The snail will reach the end when the partial sum reaches 100. In otherwords, when 100/100ths of the journy have been completed. Actually finding the number is left as an excersize for the reader :)

A better way. Rather than using a sum, integrate. The snail will reach the end after exp[100] hours.

Not too bad as an approximation, could you detail the integration ?

You seem to say the ratio of the snail position/the end of the string is the function r(t)=ln(t)/100,

but what for initial condition at t=0 ?

Ah, I see. It should be d(t)=ln(t+1)/100. Then the total time is exp[100]-1

Ages of children: They are 2, 2 and 9 years old. Why? Factorizing 36, you get several possibilities (36=2*2*3*3, and you can of course multiply with 1 as many times as you like). However, only two of these possibilities give the same sum for the ages, namely 2 2 9 and 1 6 6. Thus, one of these has to be the solution. When we get to know that there is an "oldest" whild, the solution has to be 2 2 9, as there would otherwise be TWO oldest children.

A father has three children, named Alice, Bob and Carol. Today, it's Carols first birthday. Yesterday, it was Bobs birthday, he turned six yesterday. Alice' seventh birthday is tomorrow.

I'd say that the children are 6, 6, and 1, yet it's quite clear that Alice is the eldest.

You missed a piece of info, Abigail. The mother said that "their ages are WHOLE NUMBERS", which of course means that today is everyones birthday (not just that day, but that very instant, if you worry about the decimals...). :-)

Snail problem: Dustin simply forgot a small detail: You are integrating from length l=1m to L, and get that L=exp(100) m. However, since at the start the string was 1 meter, it only takes exp(100) - 1 hours, one hours less than Dustins answer.

Sorry Dustin - I didn't notice you had already corrected it. Was just satisfied that I had solved it myself (without looking at your solution first). :-)

Well, that would mean that with (2, 2, 9) the mother gave births to twins exactly two years ago, and with (1, 6, 6), the mother gave birth to twins exactly six years ago. Either way, there are twins. And I have yet to meet a pair of twins were one of them doesn't know who is the eldest of the two. Down to the number of minutes usually.

bump