# Math Puzzle - Triangle

Puzzle

using each number once, take the numbers 1-9 and put them in a triangle with 4 slots so that each side equals 17

### Comments for Math Puzzle - Triangle

 Feb 26, 2013 Puzzle by: Staff AnswerPart IThe Solution: -----------------------------------------------Finding the solution:Use the following formula to find the number of combinations possible when selecting 4 numbers at a time (out of a group of 9 numbers) ----------------------------------------------------

 Feb 26, 2013 Puzzle by: Staff ---------------------------------------------------- Part II The number of possible combinations = 126 These are: Combinations without repetition (n=9, r=4) {1,2,3,4} {1,2,3,5} {1,2,3,6} {1,2,3,7} {1,2,3,8} {1,2,3,9} {1,2,4,5} {1,2,4,6} {1,2,4,7} {1,2,4,8} {1,2,4,9} {1,2,5,6} {1,2,5,7} {1,2,5,8} {1,2,5,9} {1,2,6,7} {1,2,6,8} {1,2,6,9} {1,2,7,8} {1,2,7,9} {1,2,8,9} {1,3,4,5} {1,3,4,6} {1,3,4,7} {1,3,4,8} {1,3,4,9} {1,3,5,6} {1,3,5,7} {1,3,5,8} {1,3,5,9} {1,3,6,7} {1,3,6,8} {1,3,6,9} {1,3,7,8} {1,3,7,9} {1,3,8,9} {1,4,5,6} {1,4,5,7} {1,4,5,8} {1,4,5,9} {1,4,6,7} {1,4,6,8} {1,4,6,9} {1,4,7,8} {1,4,7,9} {1,4,8,9} {1,5,6,7} {1,5,6,8} {1,5,6,9} {1,5,7,8} {1,5,7,9} {1,5,8,9} {1,6,7,8} {1,6,7,9} {1,6,8,9} {1,7,8,9} {2,3,4,5} {2,3,4,6} {2,3,4,7} {2,3,4,8} {2,3,4,9} {2,3,5,6} {2,3,5,7} {2,3,5,8} {2,3,5,9} {2,3,6,7} {2,3,6,8} {2,3,6,9} {2,3,7,8} {2,3,7,9} {2,3,8,9} {2,4,5,6} {2,4,5,7} {2,4,5,8} {2,4,5,9} {2,4,6,7} {2,4,6,8} {2,4,6,9} {2,4,7,8} {2,4,7,9} {2,4,8,9} {2,5,6,7} {2,5,6,8} {2,5,6,9} {2,5,7,8} {2,5,7,9} {2,5,8,9} {2,6,7,8} {2,6,7,9} {2,6,8,9} {2,7,8,9} {3,4,5,6} {3,4,5,7} {3,4,5,8} {3,4,5,9} {3,4,6,7} {3,4,6,8} {3,4,6,9} {3,4,7,8} {3,4,7,9} {3,4,8,9} {3,5,6,7} {3,5,6,8} {3,5,6,9} {3,5,7,8} {3,5,7,9} {3,5,8,9} {3,6,7,8} {3,6,7,9} {3,6,8,9} {3,7,8,9} {4,5,6,7} {4,5,6,8} {4,5,6,9} {4,5,7,8} {4,5,7,9} {4,5,8,9} {4,6,7,8} {4,6,7,9} {4,6,8,9} {4,7,8,9} {5,6,7,8} {5,6,7,9} {5,6,8,9} {5,7,8,9} {6,7,8,9} Given these combinations, identify those combinations where the sum of the integers = 17 There are only nine combinations which meet this criteria: {1,2,5,9} {1,2,6,8} {1,3,4,9} {1,3,5,8} {1,3,6,7} {1,4,5,7} {2,3,4,8} {2,3,5,7} {2,4,5,6} The numbers within each of the nine combinations can be arranged in different ways. Use the following formula to find the number of permutations possible for each of the nine combinations. ----------------------------------------------------

 Feb 26, 2013 Puzzle by: Staff ---------------------------------------------------- Part III These are: {1,2,5,9} {1,2,5,9} {1,2,9,5} {1,5,2,9} {1,5,9,2} {1,9,2,5} {1,9,5,2} {2,1,5,9} {2,1,9,5} {2,5,1,9} {2,5,9,1} {2,9,1,5} {2,9,5,1} {5,1,2,9} {5,1,9,2} {5,2,1,9} {5,2,9,1} {5,9,1,2} {5,9,2,1} {9,1,2,5} {9,1,5,2} {9,2,1,5} {9,2,5,1} {9,5,1,2} {9,5,2,1} {1,2,6,8} {1,2,6,8} {1,2,8,6} {1,6,2,8} {1,6,8,2} {1,8,2,6} {1,8,6,2} {2,1,6,8} {2,1,8,6} {2,6,1,8} {2,6,8,1} {2,8,1,6} {2,8,6,1} {6,1,2,8} {6,1,8,2} {6,2,1,8} {6,2,8,1} {6,8,1,2} {6,8,2,1} {8,1,2,6} {8,1,6,2} {8,2,1,6} {8,2,6,1} {8,6,1,2} {8,6,2,1} {1,3,4,9} {1,3,4,9} {1,3,9,4} {1,4,3,9} {1,4,9,3} {1,9,3,4} {1,9,4,3} {3,1,4,9} {3,1,9,4} {3,4,1,9} {3,4,9,1} {3,9,1,4} {3,9,4,1} {4,1,3,9} {4,1,9,3} {4,3,1,9} {4,3,9,1} {4,9,1,3} {4,9,3,1} {9,1,3,4} {9,1,4,3} {9,3,1,4} {9,3,4,1} {9,4,1,3} {9,4,3,1} {1,3,5,8} {1,3,5,8} {1,3,8,5} {1,5,3,8} {1,5,8,3} {1,8,3,5} {1,8,5,3} {3,1,5,8} {3,1,8,5} {3,5,1,8} {3,5,8,1} {3,8,1,5} {3,8,5,1} {5,1,3,8} {5,1,8,3} {5,3,1,8} {5,3,8,1} {5,8,1,3} {5,8,3,1} {8,1,3,5} {8,1,5,3} {8,3,1,5} {8,3,5,1} {8,5,1,3} {8,5,3,1} {1,3,6,7} {1,3,6,7} {1,3,7,6} {1,6,3,7} {1,6,7,3} {1,7,3,6} {1,7,6,3} {3,1,6,7} {3,1,7,6} {3,6,1,7} {3,6,7,1} {3,7,1,6} {3,7,6,1} {6,1,3,7} {6,1,7,3} {6,3,1,7} {6,3,7,1} {6,7,1,3} {6,7,3,1} {7,1,3,6} {7,1,6,3} {7,3,1,6} {7,3,6,1} {7,6,1,3} {7,6,3,1} {1,4,5,7} {1,4,5,7} {1,4,7,5} {1,5,4,7} {1,5,7,4} {1,7,4,5} {1,7,5,4} {4,1,5,7} {4,1,7,5} {4,5,1,7} {4,5,7,1} {4,7,1,5} {4,7,5,1} {5,1,4,7} {5,1,7,4} {5,4,1,7} {5,4,7,1} {5,7,1,4} {5,7,4,1} {7,1,4,5} {7,1,5,4} {7,4,1,5} {7,4,5,1} {7,5,1,4} {7,5,4,1} {2,3,4,8} {2,3,4,8} {2,3,8,4} {2,4,3,8} {2,4,8,3} {2,8,3,4} {2,8,4,3} {3,2,4,8} {3,2,8,4} {3,4,2,8} {3,4,8,2} {3,8,2,4} {3,8,4,2} {4,2,3,8} {4,2,8,3} {4,3,2,8} {4,3,8,2} {4,8,2,3} {4,8,3,2} {8,2,3,4} {8,2,4,3} {8,3,2,4} {8,3,4,2} {8,4,2,3} {8,4,3,2} {2,3,5,7} {2,3,5,7} {2,3,7,5} {2,5,3,7} {2,5,7,3} {2,7,3,5} {2,7,5,3} {3,2,5,7} {3,2,7,5} {3,5,2,7} {3,5,7,2} {3,7,2,5} {3,7,5,2} {5,2,3,7} {5,2,7,3} {5,3,2,7} {5,3,7,2} {5,7,2,3} {5,7,3,2} {7,2,3,5} {7,2,5,3} {7,3,2,5} {7,3,5,2} {7,5,2,3} {7,5,3,2} {2,4,5,6} {2,4,5,6} {2,4,6,5} {2,5,4,6} {2,5,6,4} {2,6,4,5} {2,6,5,4} {4,2,5,6} {4,2,6,5} {4,5,2,6} {4,5,6,2} {4,6,2,5} {4,6,5,2} {5,2,4,6} {5,2,6,4} {5,4,2,6} {5,4,6,2} {5,6,2,4} {5,6,4,2} {6,2,4,5} {6,2,5,4} {6,4,2,5} {6,4,5,2} {6,5,2,4} {6,5,4,2} ----------------------------------------------------

 Feb 26, 2013 Puzzle by: Staff ---------------------------------------------------- Part IV Now, eliminate entries with duplicate end points to reduce the number of possibilities: After the duplicate end points are eliminated, the number of possibilities is greatly reduced: {1,2,5,9} {1,2,5,9} {1,2,9,5} {1,5,9,2} {2,1,5,9} {2,1,9,5} {5,1,2,9} {1,2,6,8} {1,2,6,8} {1,2,8,6} {1,6,8,2} {2,1,6,8} {2,1,8,6} {6,1,2,8 {1,3,4,9} {1,3,4,9} {1,3,9,4} {1,4,9,3} {3,1,4,9} {3,1,9,4}{4,1,3,9} {1,3,5,8} {1,3,5,8} {1,3,8,5} {1,5,8,3}{3,1,5,8} {3,1,8,5}{5,1,3,8} {1,3,6,7} {1,3,6,7} {1,3,7,6} {1,6,7,3} {3,1,6,7} {3,1,7,6} {6,1,3,7} {1,4,5,7} {1,4,5,7} {1,4,7,5} {1,5,7,4} {4,1,5,7} {4,1,7,5} {5,1,4,7} {2,3,4,8} {2,3,4,8} {2,3,8,4} {2,4,8,3} {3,2,4,8} {3,2,8,4} {4,2,3,8} {2,3,5,7} {2,3,5,7} {2,3,7,5} {2,5,7,3} {3,2,5,7} {3,2,7,5} {5,2,3,7} {2,4,5,6} {2,4,5,6} {2,4,6,5} {2,5,6,4} {4,2,5,6} {4,2,6,5} {5,2,4,6} As a last step, match the various possibilities with one another until you get a match. Refer to the top of this post for the final solution. Thanks for writing. Staff www.solving-math-problems.com

 May 29, 2020 More than one solution? NEW by: yo-HO-Mathy 1 9 6 5 7 2 4 8 3 Am i missing something, seems theres is more than one answer

 May 29, 2020 More than one solution? by: yo-HO-Mathy 1 9 6 5 7 2 4 8 3 aARRrrrrrghh, Ye am i missin' somethin'¿?, seems thars be more than one answer. Off t' thee bayesian of pirates now t' collect me reward th' Math Pirate

 Aug 21, 2020 other solutions by: Siraj Solution 1 1, 2, 3 being vertices Side A 1+9+5+2=17 Side B 2+4+8+3=17 Side C 1+6+7+3=17 Solution 2 1, 4, 7 being vertices of triangle Side A 1+8+6+4=19 Side B 4+3+5+7=19 Side C 1+2+9+7=19 Solution 3 2, 5, 8 being vertices of triangle Side A 2+9+4+5=20 Side B 5+6+1+9=20 Side C 2+3+7+8=20 Solution 4 8, 7, 3 as vertices Side A 8+1+5+7=21 Side B 7+9+2+3=21 Side C 8+6+4+3=21 Solution 5 9, 8, 7 being vertices Side A 9+1+5+8=23 Side B 8+6+2+7=23 Side C 9+4+3+7