*Originally posted by Aetherael*

**i think his point was that your method can't possibly be correct because you could use it to find an "answer" for a case that can't possibly be true. by showing your method's failure at the extremal value, he showed a flaw in the logic of your argument that should be re-examined.
**

yes, the calculation you performed outputted the correct answer in this ...[text shortened]... ince your method fails to compute accurately for higher percentages (e.g. 90%, 100%, etc.).

Look, even Einstein manipulated things to fit his basic design. Discounting an answer that is impossible is just good judgement. This method may not be clean, but it does produce the correct answers.

This method relies on computational ratios. Ratios have calculations built into them that provide us with short-cuts. If I told you I have 2 apples for every 3 apples you have, we could write that as 2/3. Automatically we know that I have .66 apples for every 1 you have. If someone wanted to know how many apples I had if you had 10 apples, we'd only have to mulitply .66 by 10 to get the answer. The ratio (or percentage if you prefer to think of it that way) calculates the answer for us. In the same sense, we can use ratios to determine how much more of something we need if we know how much we have. In this case we knew how much of a confidence level we had with 4 boxes (12.5% ) so all we had to do was perform a ratio calculation to determine how much more we needed.

The question usually provides some inherent answers too. In this case 50% and 90% were asked for. 50 and 90 give you nice round numbers of boxes. The "correct" answer method provided by mtthw (i think) it was was fine...but use it for say 65% or 85%. Will that answer give you a nice round number of boxes?

The question is providing secret information that you can use to build a ratio calculation. You just have to be prepared to reject an answer that you know cannot be correct...in this case the case for 100% (and 0% )

The question really is giving away the answer. Really, the key here is the boxes. You cannot have parts of a boxes. You can only have whole boxes. So you can either have 4 boxes or 5 boxes or 10 boxes or 11 boxes etc. You cannot have 11.4 boxes. So, really, the question should have been phrased as,

"you have 13 boxes. there are 4 prizes. At what confidence level are you at that you will have all 4 prizes. This way you have no idea what the answer will be...it could be 90%, it could be 91 it could be 84..hell it could be 21.5%, you have no idea until you calculate it.

But, ask how many boxes you need to get to a 90% confidence level and you KNOW that the asnswer is going to be a whole number because you can't have a decimal number for an answer since a decimal number would mean you don't have a whole box.