ParaLogic

Hah! Now we bring out the monopoly money!

Oops. I accidentally (mentally) switched Eric/Adam's names when I read the first few lines.

The question 'yes?' is rather vague. I have no idea what he's trying to ask.

uno>tres>cuatro<=>seis dos>tres>cuatro<=>seis cinco<=>cinco siete>cinco<=>cinco ocho>cuatro<=>seis nueve>cinco<=>seis diez>cuatro<=>seis once, doce, trece, catorce, quince, dieciseis, diecisiete ... So it's nowhere as neat. Numbers either end up in the 4=6 loop or at 5. Now how about Roman Numerals?

At first, I thought this 35 page long argument was ridiculous, but after reading bona/syon's posts above, I can understand some of the trouble surrounding the ambiguity of the question. This is the way I see it: There are four possibilities for boy/girl combinations, as mentioned several times by now (I imagine): BB BG GB GG Note that this categorization does take into account the order of the children. We are shown that one of the children is a girl, which of course eliminates the first combination.This is the point where people jump to the answer of 1/3, since there only seem to be three combinations remaining. However, as I stated before, order does matter if you look at the problem this way. Therefore, there are still four possibilities: G1B2 G2B1 G1G2 G2G1 Where the number indicates order. The girl we see can be either the elder (G1) or younger (G2) sister, so we must look at both possibilities equally. Thus, the probability stands at 1/2, regardless of the order of birth. Another way to look at this is to completely disregard order in all of the cases. The resulting combinations are: BB GB (same as BG!) GG When BB is eliminated, the probability of GG remains at 1/2.

Wow! I was actually thinking about this exact situation a couple of weeks ago, and I noticed the same convergence. But I didn't consider proving it...

I think that's the best solution if you don't re-arrange any pieces until the end, but I didn't say you couldn't..? I'll just share my solutions for #7 now, since this thread has passed on.

Bah, just eat them all!

I don't like the implications of negative angles, but if you use them, then As for irrational numbers...well I don't (want to) know.