80 - 99 D under 80 Horrible!! Partial Solutions for some of the previous questions A-1 The other five solutions use the following groups of 3x5 Rectangles. pieces: {P, {N, {P, {F, and {L, U, V}, P, U}, U, Y}, P, U}, P, V}. A-2 (b) There are 2 solutions, one for the and 4x5 Rectangles. P the (c) One solution uses {L, (d) One solution uses {F, U. P, V, Y}. L, U, V}. A-3 (b) Solutions for the and If the 5 x 5 Squares. F, P, T, U, V, W, Z. rectangle does not contain the then solutions only exist for the I, P, U, and W, Z. A-4 Many Rectangles. Size of Rectangle Number of Solutions 1 x 5 1 3 x 5 7 2 x 10 2 4 x 5 50 5 x 5 107 3 x 10 145 5 x 6 541 5 x 7 1396 4 x 10 2085 5 x 8 3408 3 x 15 201 5 x 9 5902 5 x 10 6951 5 x 11 4103 A-5 {F, Congruent Groups. T}
80 - 99 D under 80 Horrible!! Partial Solutions for some of the previous questions A-1 3x5 Rectangles. The other five solutions use the following groups of pieces: {P, U, V}, {N, P, U}, {P, U, Y}, {F, P, U}, and {L, P, V}. A-2 4x5 Rectangles. (b) There are 2 solutions, one for the P and the U. (c) One solution uses {L, P, V, Y}. (d) One solution uses {F, L, U, V}. A-3 5 x 5 Squares. (b) Solutions for the F, P, T, U, V, W, and Z. If the rectangle does not contain the I, then solutions only exist for the P, U, W, and Z. A-4 Many Rectangles. Size of Rectangle Number of Solutions 1 x 5 1 3 x 5 7 2 x 10 2 4 x 5 50 5 x 5 107 3 x 10 145 5 x 6 541 5 x 7 1396 4 x 10 2085 5 x 8 3408 3 x 15 201 5 x 9 5902 5 x 10 6951 5 x 11 4103 A-5 Congruent Groups. {F, T}
pentominos-2.docx