David and Ben each played one game of darts and then discussed their scores.
Ben: "We both scored 110 points, including the bonus. But our dart boards don't look the same."
David: "That's not suprising. There are lots of ways to duplicate dart scores."
How many different arrangements of the darts are there that have a score of 110? An arrangement is different if the numbers in the corners are different, or if the numbers between two corner numbers are different.
Rules
1. Each of the nine darts must land inside a circle on the dart board.
2. No two darts can land in the same circle.
3. Add the numbers on the four darts on each side of the triangular board.
4. Your score is the sum of the three side sums, plus a bonus of 50 points if all three sides have the same sum.
Darts
Dart 1= 1 point
Dart 2= 2 points
Dart 3= 3 points
Dart 4= 4 points
Dart 5= 5 points
Dart 6= 6 points
Dart 7= 7 points
Dart 8= 8 points
Dart 9= 9 points
Dart board is 9 circles in a triangle - four on each side.
Reference from Greenes, Carol, Linda Schulman, Rika Spungin, Suzanne Chapin, Carol Findell. Mathletics: Gold Metal Problems. Providence RI: Janson Publications Inc., 1990.