bonanova

I know the formatting wasn't perfect but I tried. Bingo. Good job.

Thirteen balls, one is heavier or lighter = 26 possibilities. Each weighing has three possible outcomes, and 33 = 27 distinguishable cases. Are we sure this is impossible?

If color alternates, you save only 1 while dooming 18. <_<

Am I on the right track? I'll keep working on the placement of the numbers. You are correct.

A repasts' agenda begins all things here. Move back to front and add you's "be" ... <-[yeah, right: the new word goes there] You must, you see, for here rhymes belong or else you'll discover that it is all wrong. Now add a "look"; but "see" only a ghost or a hint, or a border, if that, at most. Add K to produce the young Spaniard's tool which aided him recently down under to rule. Move back to front, and again add an R to get one who finds his prey, be't near or far. Drop Spaniard's K, and also first's last to get one whose livelihood's to always be fast. Remove now the C, and flip middle two and you will discover what's following you. Then toss out the A, and give things a shake And, Lo and behold: you've made a mistake!

I had days like that ... before I retired. Nice one!

What animal has the head of an elephant, the body of an owl and the tail of a mouse?

The question would be a lot harder if you wanted to know the filled in hexagon :-) Good point. Go for it. Nice analysys btw. And, welcome to the Den

Arrange six quarters around the perimeter of a central quarter, and twelve more around the new perimeter. That makes six rows of 3 coins, six rows of 4 coins and three rows of 5 coins. Number each coin with a different number from 1-19 so that the same sum is achieved along all fifteen rows. What is that sum? OK now that we have that settled, find the numbers.

Nice!

That's a 3. And you could do that with matches.

EventHorizon: Eraser: yes - as if you had matches, you could move some. Two straight edges: No. The straight edge is just to align the matches, if we were using matches, so it's just to draw lines in this case. Use it to draw a circle: no. the intent is not to construct a figure. G Threat: Yes it's a polygon but I don't know how you'd guarantee the area is integral Y-san: Apology was sweet, but not necessary. Since I don't smoke or otherwise set fire to things, the matches are no loss. And I agree, the limits should be clear. The best puzzles, I've found, have a bit of genius in the wording. I didn't have the needed genius on this one. Now to the answers. EH: I'd love to see a sketch, cuz I got lost when you mentioned two lines of length 5. Y-san: One word - Bingo. Still a bit of a puzzle to word the question and require this solution. Can't rule out others by saying convex or rectilinear. I still think this is the only solution that you could really do with matches. Fairly easy to eyeball vertical 3, horizontal 4, line up the 5, then dent in the corner. Rhombus seemed qualitatively harder, to me at least. I read the puzzle a couple days ago and liked it, even tho it didnt come with a solution. In fact, it asked to make A=4, which I envisioned as 345 with two bottom squares missing. So You did it one better. I had to draw it to convince myself. Nice.

Averaging two speeds run for identical time intervals is ok. But ... Read the OP. There is no mention of 3 miles or 6 miles - it's 3 mph and 6 mph. It's the distances that are identical. Since this puzzle has appeared many times in this forum, it's locked.

That seems to work. B doesn't need to roll, tho. Nice.

A unit cube has area 6 and volume 1. And it's a polyhedron, not a polygon.

Yes. I'm having a hard time ruling out rhombus solutions. You need to make angles whose sines have rational values - tough to know when you have done that. But to be fair, you have to eyeball horizontal and vertical to know when a square is exact. OK. Truce. Let's burn the matches, and state the idea differently. You are given a sheet of ruled paper, with horizontal and vertical lines 1" apart. no other notion of distance or angle [don't tear off a piece of the paper to use as a ruler] an unmarked straight edge a sharp pencil - which writes only on paper [i.e. won't write on straight edges] Draw a polygonwhose diameter everywhere is positive definite [ruling out woon's polygons and a 0x6 rectangle] all of whose sides are integral length whose perimeter is 12 whose area is integral What is the minimum area you can achieve?

Already posted with name spelled differently.

Yes. Is it possible to make one with Area=4?

No stacking. End-to-end.

On the grave of Diophantes, the Alexandrian mathematician, the following inscription appears: This stone marks the grave of Diophantes. If you solve this riddle, you will know his age. He spent one-sixth of his life as a child, Then one-twelfth as a youth. He was married for one-seventh of his life. Five years after he married, his son was born. Fate overtook his beloved child; he died When he was half the age of his father. Four more years did the father live Before reaching the end of this life. How long did Diophantes live?

Prove it's not, based on "scarce"ness.