Mathematical Gems, Issue 2Mathematical Association of America, 1976 - Combinatorial analysis |
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Page 58
... tetrominoes ( see Figure 36 ) . There are 12 pentominoes ( Figure 37 ) and 35 hexominoes , but no general formula is known for the number of " n - ominoes " which can be made from n squares . We note that for greater n ( > 7 ) it is not ...
... tetrominoes ( see Figure 36 ) . There are 12 pentominoes ( Figure 37 ) and 35 hexominoes , but no general formula is known for the number of " n - ominoes " which can be made from n squares . We note that for greater n ( > 7 ) it is not ...
Page 63
... tetrominoes . However , try as you will , there is no way to pack a 10 × 10 rectangle with pieces of this type . This is a consequence of the following theorem : THEOREM . Rectangles which can be packed with L - tetrominoes always need ...
... tetrominoes . However , try as you will , there is no way to pack a 10 × 10 rectangle with pieces of this type . This is a consequence of the following theorem : THEOREM . Rectangles which can be packed with L - tetrominoes always need ...
Page 65
... tetrominoes , ab / 4 , is an even number , we see that ab must be a multiple of 8. It can be shown that the L - tetromino packs an a × b rectangle if and only if a , b > 1 and 8 divides ab . In 1965 , D. W. Walkup proved the similar ...
... tetrominoes , ab / 4 , is an even number , we see that ab must be a multiple of 8. It can be shown that the L - tetromino packs an a × b rectangle if and only if a , b > 1 and 8 divides ab . In 1965 , D. W. Walkup proved the similar ...
Contents
CHAPTER PAGE 1 Three Surprises from Combinatorics and Number Theory | 1 |
Four Minor Gems from Geometry | 10 |
A Problem in CheckerJumping | 23 |
Copyright | |
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1-factor a₁ a₂ Accordingly Amer attainable score beads BICENTRIC POLYGONS black edges circumcenter circumcircle collinear column complete graph configuration congruent Consequently contains contradiction copies deleted diagonal digits distance can occur divides dominoes eight-point circle equal exceed Figure Gabriel Lamé gives graph G harmonic bricks harmonic series hexominoes implying incircle integer intersection isosceles 6-point isosceles tetrahedron key multiple Klarner L-tromino lattice point layers least line ax Math monomino Monthly n-gon natural numbers necklaces number of vertices obtain odd block odd components odd number odd prime P₁ pack the line packable pair Paul Erdös plane polyominoes prime number problem proof proved quadrilateral rectangle red edges relatively prime result segments sides Similarly Slothouber-Graatsma Puzzle spheres subset Suppose tangent tetrahedron tetrominoes theorem total number tromino unattainable unit cubes vertex Wilson's theorem yields