Three L-tetraminoes
Here is a cool puzzle I heard from Tiago Hirth at the last Gathering for Gardner, who in turn heard it from Donald Bell.
Puzzle. You have three L-tetrominoes. Arrange them on a plane without overlaps so that the resulting shape has a line of symmetry.
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Lazar Ilic:
Lazy Loves Fish
ZZZ-
X-ZY
X–Y
XXYY
ZZZ–
9 June 2024, 5:53 amZ-YYY
XXY–
-X—
-X—
Donald Bell:
Tanya
17 June 2024, 4:37 pmAnother one of my symmetry puzzles you might enjoy. This time there are only two pieces.
Make a 30-60-90 triangle (ie half an equilateral triangle)
Divide it into two 30-60-90 triangles of different sizes by dropping a perpendicular from the right angled corner to the opposite sidew.
Put these two pieces together to make a symmetrical shape.
There are two solutions.
Donald
Kai:
@Donald:
Let the lengths of the six sides be 1, root(3) x 2, 2, 2root(3), 3 respectively. The two longest sides, i.e., 2root(3) and 3, have no counterparts so that the reflection axe must pass through the both sides. Then it is not difficult to find the two solutions. One is obtained by placing the two right angles together and the two sides of root(3) colinear. The other is obtained by placing the two 30-deg angles together and the two sides 2 and 3 overlapped.
21 June 2024, 2:03 pm