Printing Error: First observe that 79 can only be 9x8+7 in some order, and with two of those numbers unavailable, 80 can only be 8x2x5 in some order, so we can place the 8. If the 9 goes at the bottom, 31 can only be 4+3x9 but 1, 6, and 7 cannot make 27 so this is wrong and 7 goes at the bottom. Now 31 can be 4x6+7 or 3+4x7. 27 can be 1x3x9 or 3x6+9. The only way to avoid duplication is to use the first of each pair of possibilities. We still have to properly order the first two numbers of each row. 9 can be made as 3+2+4, 1+2+6, 1+2x4, or 1x5+4. 21 can be made as 3x5+6 or 1+5x4. Only 3x5+6 and 1+2x4 avoid duplication. 3 x 1 x 9 =27 x + x 5 x 2 x 8 =80 + x + 6 x 4 + 7 =31 = = = 21 9 79 Joseph DeVincentis ------------------------------------------------- Here's a solution I found to this puzzle: 3 x 1 x 9 + + + 5 x 2 x 8 x + + 4 x 6 + 7 In case the ascii formatting doesn't work, here's what i have, row by row: "3 times 1 times 9 row plus plus plus row 5 times 2 times 8 row times plus plus row 4 times 6 plus 7" Thanks for your time, Joey ------------------------------------------------ 3 * 1 * 9 =27 * + * 5 * 2 * 8 =80 + * + 6 * 4 + 7 =31 = = = 21 9 79 John Dalbec ------------------------------------------------ Hi Ed, Here's a solution to Bryce Herdt's Printing Problem problem. 3 * 1 * 9 = 27 * + + 5 * 2 * 8 = 80 + * + 6 * 4 + 7 = 31 = = = 21 9 79 Thanks again to you and Bryce for the entertainment, Matt Sheppeck ------------------------------------------------ Hi Ed, This little puzzle stumped me for a while. However, 80 can be assembled only with the 5*2*8 and then 79 has only one solution also. 3 * 1 * 9 * + * 5 * 2 * 8 + * + 6 * 4 + 7 Dick Saunders Jr. ------------------------------------------------- Solution: 3 x 1 x 9 = 27 x + x 5 x 2 x 8 = 80 + x + 6 x 4 + 7 = 31 = = = 21 9 79 Alan Lemm -------------------------------------------------- 3 * 1 * 9 =27 * + * 5 * 2 * 8 =80 + * + 6 * 4 + 7 =31 = = = 21 9 79 This assumes normal operator precedence of * before + Kirk Bresniker -------------------------------------------------- In rows: 3x1x9=27 5x2x8=80 6x4+7=31 In columns: 3x5+6=21 1+2x4=9 6x4+7=1 Simple but ingenious because pleasant for solving - logically, step by step. Congratulations! Marek Penszko Warsaw, Poland --------------------------------------------------- Printing Error Answer: 3x1x9 x + x 5x2x8 + x + 6x4x7 Colin Sturm Michael Matlock --------------------------------------------------- I don't know if the formating will work, but here are the equations Verticle from left to right: (3 * 5) + 6 = 21 1 + (2 * 4) = 9 (9 * 8) + 7 = 79 Horizontal from top to bottom: 3 * 1 * 9 = 27 5 * 2 * 8 = 80 (6 * 4) + 7 = 31 So the grid looks like: 319 528 647 and the operations * * * + * * * + * + * + Christopher Johnson ------------------------------------------------------ 3 * 1 * 9 = 27 * + * 5 * 2 * 8 = 80 + * + 6 * 4 + 7 = 31 = = = 21 9 79 Wang Zirui ------------------------------------------------------ Hi Ed, Here's the solution to Bryce Herdt's puzzle: 3 x 1 x 9 x + x 5 x 2 x 8 + x + 6 x 4 + 7 Daniel Scher