Tuesday puzzle

Re: Tuesday puzzle

Thomas Skaggs, Foothills of Mount Level

Getting 4 would require one to think "internally".

T.

Re: Tuesday puzzle

Bill Earl

The solution for 4 is sin(pi/3) matchsticks tall.

For 6, it would be 4(sin(pi/3))/3 matchsticks.

Maybe

Alex Y

but I don't follow your answer.

You're making me work!

Alex Y

Or more accurately, my pride prevents my grabbing the CRC or googling to check your answers.

The solution for 4 is sin(pi/3) matchsticks tall.

I think that sin(pi/3) is sqrt(3)/2. The solution I am thinking of is sqrt(6)/3 tall. I'll look forward to seeing the solution you have in mind. The one I am thinking of (for four triangles) creates equal-sized triangles with no unused matches or portions of matches.

For 6, it would be 4(sin(pi/3))/3 matchsticks.

David would be proud of your finding this solution, but you need to recount the equilateral triangles here to increase your claim!

Re: You're making me work!

Bill Earl

Aha! Now with the benefit of coffee, I see that my first solution actually has 6 triangles, and David's has 8. I guess I still need to find one with just 4.

Re: You're making me work!

Bill Earl

OK: I had to add another row and column to the transform matrix, but I've got a solid solution.

Re: You're making me work!

Alex Y

Well, I don't remember enough about transformation matrices, but if you say you have a solid solution, I'm sure it is the same as the one I am thinking of, the name of which includes the name of a fresh-water fish or a Greek reference to the number of triangles.

Re: Tuesday puzzle

karl jr

I can see a solution with 4 equilateral triangles, but I can't visualize a solution with more than 4.

Re: You're making me work!

Bill Earl

One of "Bucky's" favorite shapes. Pharaohs would have liked them too if they weren't so square.

Re: Tuesday puzzle

Jerry Glaser

Isn't the solution a three dimensional figure with the base an equilateral triangle of the three matchsticks and the remaining three sticks at each corner standing up to form a pyramid. You then have four equilateral triangles.

Solutions

Alex Y

Congrats to Bill, Jerry, and maybe Karl for getting the basic 4-triangle answer.

The key is to think in three dimensions, as described by Jerry. It is the "solid" answer Bill referred to, a tetrahedron--think of it as a pyramid with a triangular base.

Bill got two additional answers that work in 2-D, with matches overlapping:

Form two triangles, one on top of the other. Flip the top one (or rotate it 60 degrees) and you have a Star of David, with six equilateral triangular points, as well as the two original triangles.

"Push down" a point of one of the triangles so that its vertex is at midpoint of the base of the other large triangle, and you have four small triangles (but larger than the Star of David points) as well as the original two.

Thomas: I never saw what you meant by the think internally comment, so my apologies if you had a solution that I gave short shrift.