BMAD

Are the two lists separate? I interrupted the OP to mean one mega list with whoever identifies the number that makes 15 (from 2 additional numbers) is the winner.

It is solved. People stop reading forums once they are marked that way I found, so I tend to draw out marking them as such right away.

Suppose you have a rectangle with dimensions 2x2x4. Making 1 slice, what 2-d shapes can be formed at the site of the cut? What if you make 2 cuts?

They are greatly missed

You are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will grant you three wishes. The only catch is that the bottle must thereafter be resold for a price smaller than what you paid for it, informing the buyer of the same requirement, or you will be condemned to live out the rest of your days in excruciating torment. How much should you buy the lamp for?

How many times do you need to fold a piece of paper (A4 size) in half, to make it reach the moon? Assume that the paper is 0.1 mm thick and that the distance to the moon is 384,403 kilometers (238,857 miles) — the accepted average.

Back around the time I first joined brainden I posted a favorite puzzle of mine: It didn't take long for the brainden elite to crack it using calculus. Surprisingly and grateful though, I also saw the use of geometry (my favorite subject!!) to crack it too and as a result, I have been hooked to this site ever since. I am now modifying the problem slightly. The challenge here of course is to not use calculus except to verify if needed. Here we go: Suppose the area of the innermost intersection is Pi, can we extrapolate back to the circle's original radius?

hmm... Being a mathematician, logician and a perfectionist (all-in-one), I disagree

Wouldn't a triangle with one side = 0 collapse into a line segment or 2 co-located line segments ?? I don't have an answer, but I suspect that is NOT the answer that BMAD is looking for - but it made me chuckle [thanks]. Either a degenerate triangle, as gavinksong suggests, where a2 + 0 = c2,

I have two 'unfixable' clocks: one doesn't run at all and is stuck at 12:00, and the other loses a minute a day. Which would you prefer?

What can you conclude from the following statements? (1) Babies are illogical. (2) Nobody is despised who can manage a crocodile. (3) Illogical persons are despised.

Is there any triangle other than a right-angled triangle that possesses the sum of squares property (pythagorean theorem)? What about other polygons constructed similarly on three sides of a right-angled triangle? Is the area of the figure constructed on the hypotenuse equal to the sum of the figures constructed on the other two sides or is the result only for squares?

*bump*

Casimiro went for a walk one day and came to an orange grove. The oranges looked tempting, so he asked the owner for one. The owner agreed to give him an orange, but Casimiro would need to follow certain rules. He would have to pick a number of oranges and go through three gates. At each gate Casimiro would need to leave half the number of oranges he was carrying plus half of an orange, all without cutting any of the fruit. How many oranges did Casimiro pick so that after going through the three gates, he would have the one orange he asked for?

anything else we can say about that number?

Hint... Try it for numbers 1-10 see what happens. Then try it for 1-20 and see what happens. Then generalize based on your conclusion.

Write a list from 1 to 100. Pick two numbers at random Sum the two numbers, find the product of the two numbers Sum the above two numbers Erase the two chosen numbers from the list Add the sum of the two numbers to the list Repeat until there is only one number. Repeat the above process multiple times. Is it the same number? Do the numbers center around a point? Bimodal? analyze.

I agree gavinksong. Sorry for not committing before. Initially I found your solution to be merely an alternative to the original. But after consideration, I think yours is better. I have switch to gavinksong's solution as it appears to be more robust. I am open to arguments for/against either TSLF or Gavin's or another better option if anyone has interest.

Are you saying plasmid's post is the correct answer? I am saying his rephrasing of what you attempted to clarify is an appropriate rephrasing.

math is permitted

well done.

to answer the spoiler question, i believe the circle radius needs to be greater than (equal) 1/2 the distance between two points.

does this approach hold if the pentagon is not regular or convex?