Geometry Forum - Problem of the Week
Solutions - Polyiamonds, Oct. 3-7, 1994
Annie says:A good response from our readership this week, including a number of first-time participants - welcome!
This problem was solved by trial and error. Almost all are variations of the same solution, and a number of the participants created notation to indicate the positions of the pieces - whether they were flipped or rotated. Very nice!
One student, Sam Brenner, sent in an answer which used one piece twice. While that wasn't the intention of the question, it certainly isn't against the rules. Can anyone find other answers that use one or more pieces more than once? Sam's solution is listed last.
Zac Derr
I started by cutting out six points out of three by five cards. I knew how big to make the points because piece seven is one of the points with a triangle missing at the base. I then put the points together to make the star. After that I just filled it in like a puzzle by trial and error. The general placement of the pieces is below. O means the piece has been turned over.
12 O
2 11
5 8
3 O 7
10 O
Colorado Creative Education Group
3
2 5
10
8* 7**
12 11*
* = flipped pieces, ** = turned piece
I hope this works. If not please ask for another sketch. they did
solve this. We had lots of success with this week's POW.
Younger learners listed their names in order of who contributed
most to solving the POW. Brian Quinn (11 yrs.), Ryan Foster (10 yrs),
Michael Cragg (12), Lima Manning (12), Lauren McEvoy (11), Julia
Oppenheimer (9), Louise Schumm (9). The other younger group were:
Alexander Cragg (11), Hale Manning (11) and Nick Rung (11). Older
learners who solved the POW were: Isaac Bogart (17 yrs), Dannie
Kobrin (17), Eli Wolcott (15), and Dan Hurlbutt (17).
Kelley Schmidt, Lauren St.Clair, Jen Hinkel & Kristin Burton, and Erin Foley
11
7 12
8
10 2
5
3
Others solutions were variations of this answer.
Michele Gibney
I first drew a six pointed star and then I started putting in the different numbers of triangles. I put the numbers on the star for you to see. It took me about twenty minutes to do this problem.First, I found that the little triangles were not actually equilateral triangles like they were supposed to be. So I made new shapes with the equilateral triangles. Then I made a six point star with 48 equilateral triangles in it. Then it was just a matter of trying to put the triangles into the star. I did it mostly by trial and error. However with actual equilateral triangles, it only took me two tries to get the combination. My solution is below:
7
11 10
8 3
12 5
2
It looks much better when you draw it, but I can't. So, I hope
you can understand from this rather crude diagram.
Michael Summers
Michael Summers' solution did not come through with GeoExplorer. Here is his solution:
3
5
2 10
8
12 7
11
Nicole McKeown
To solve the problem of the week, I used trial and error. That is all I did. It took me about two hours. Number eight is in the middle. Eleven is at the top. Seven is at top left. Twelve is at top right. Ten is at lower left. Two is at lower right. Three is at the bottom. My name is Nicole McKeown. I am fifteen years old. I really enjoy doing math.[in response to a plea from me, Nicole sent the following:]
I realize that this is late, but I decided to draw a picture. I will send the picture next mail. I figured out the piece I was missing. It is five, at the lower right.
*11
7 12
*8
10 5 *2
3
Joe Bailey
Hi. This is first time that I am using the Next Step software to answer a problem of the week. It sounds like fun and here is my solution.
3
5
8 10
12 2
7
11
Lisa Moore
The first step took in solving this problem was to draw a picture of the star of David. After I did this, I realized that I could not use piece 4 (the hexagon). I then used the other pieces to try and fill in the star. You could probably call this a trial & error method. I came up with this solution:
11
7 12
8
10 2
3 5
Anthony DeLuca
I drew a six sided star first and worked the problem like a puzzle. It seemed a lot easier that way. I hope to talk to you sometime soon with another solution to the problem of the week.
11
7 12
8
10 5 2
3
Missy Kochanowski and Melissa Hudak
The first thing I did to try and get the answer to the problem of the week was use trial and error, but that was taking up to much time. So I drew a six pointed star and tried to fit the pieces into my drawing. This is what my conclusion was:
11
7 8 12
10 5 2
3
The shape 11 was on the opposite side, the shape 8, 2, 10 were
also on their opposite sides. The shape number 3 was up side down. This was my main
way of getting the answer. I used trial and error even though I drew a figure to help me. If
I would not have drawn that figure it would have been really hard to figure out.
Samantha Brenner
The pieces should be configured as follows:
12
2 11
8 10
7 10
3
Five of the pieces are turned over -- the 12, 8, both 10's and
the 3.
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