bonanova

You are given a point M and an angle C in the plane. Using a ruler and a compass, draw a line through the point M that cuts from the angle C a triangle with a given perimeter p. In the figure below, a green line has been drawn through the point M that creates a green triangle with the angle C. The task is to create such a triangle that will have a given perimeter p. The ruler you are given functions as a straight edge and also allows you to measure distances.

The omitted rule is the smallest card beats (only) the highest card. Should we assume the students are now playing without that rule in effect?

OK so it's not that hard. There are two parts: (1) Magenta area and (2) total area.

First thoughts.

On further review, Rob and I are both right. But Rob is "righter:

White KB begins on KB1, or in standard chess notation on f1, a white square. The white KN is at its side on square g1.

In one of the Bard's best thought of tragedies, our insistent hero, Hamlet, queries on two fronts about how life turns rotten. A thin man ran; makes a large stride; left planet, pins flag on moon! On to Mars!

An Anagram, as we all know, is a word or phrase made by transposing or rearranging the letters of another word or phrase. The following phrases can be anagrammed into their definition or description. Honor code is in force: Dirty Room (Clue: single word beginning with D.)A Rope Ends ItHere Come DotsCash Lost in 'emIs No AmityAlas! No More Z'sGenuine ClassIs No MealLarge Picture Halls, I betI'm a Dot in PlaceThat Queer ShakeTwelve plus oneAccord not in it

Simulation is the only I know.

Thirty or so years ago...

TSLF has it. Nicely put into words.

First reaction is that must hurt. If I wanted to be nit-picky (me?) the head of one might precede that of the other. Point taken.

To be more specific, you can draw a line segment between two existing points or extend an existing line segment. So I guess the OP should say you also have a pencil. That should do it. The straight edge has no markings - it's not a ruler; you can't twirl it like a compass ... etc.

Could that result be programmed recursively, rather than going for closed form?

I know the answer approximately from simulations. I'm still scratching my head about calculating it. I agree with plasmid's last statement, but how to calculate his "given" puzzles me.

Are we assuming a mammalian birth process? Then splitting is in utero, and age origin is time of birth.

Just to be clear about the order of subtraction. In your inequality, does A - B - C - D = A - (B + C + D)?

Standard. But I think the cat is out of the bag. Still getting used to the new posting protocol.

Shamelessly bumping this thread.

shepster has it.

OK well since I will define this puzzle not to be an algebra class assignment ... hhh3 has the correct answer. Anyone else see why?

I see what you mean. Kind of like being able to draw an nth-order polynomial through any set of n points.

I thought my series was unique, too.