perplexus.info :: Shapes : Triangles to Squares

Triangles to Squares (Posted on 2003-01-20)

You have 8 wooden right-angle isosceles triangles (the lengths of the two lines that make up the right angle are equal). These are numbered from 1 to 8. Every single triangle is equal in size. Using these triangles how many DIFFERENT squares can you make. (Not neccesarily all at once)

Note: A square must be entirely wooden in order for it count. A square cannot have the exact same combination of triangles that have already been used.e.g if you used triangles 1 and 2 in one combination you can never have a square made from only triangles 1 and 2. (However triangles 1 and 3 would make a distinct square)

Submitted by Alan

Rating: 3.6000 (5 votes)

Solution: (Hide)

Well first you must realize that there are 3 ways to make these triangles.
1.Two triangles with thier long sides touching. There are 28 different squares you can make using 2 trangles.
2.Four triangles with all their right angles touching. There are 70
3.All 8 triangles put together(this is done by having all the triangles be put into squares of two then those 4 squares being put into a supersquare)There is only 1.
So altogether there are (28+70+1) triangles that cane be made. So that means there are 99 different squares you can make.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
nice	Charming	2003-04-07 07:47:58
re: solution?	terry	2003-01-23 02:37:51
solution?	epperson	2003-01-22 20:15:01
re(2): Solution?	TomM	2003-01-21 03:27:54
re(2): Solution?	Alan	2003-01-20 11:08:10
re: Solution?	friedlinguini	2003-01-20 10:51:55
Solution?	fwaff	2003-01-20 06:13:11

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