+647 Let a, b, c, d, and e be positive integers. The sum of the four numbers on each of the five segments connecting "points" of the star is 28. What is the value of the sum a + b + c + d + e?
+9479 Here's another interpretation.
a + 1 + 4 + c = 28 → a + c = 23
a + 3 + 5 + d = 28 → a + d = 20
b + 4 + 2 + d = 28 → b + d = 22
b + 1 + 3 + e = 28 → b + e = 24
c + 2 + 5 + e = 28 → c + e = 21 Add all five of these equations together to get...
2a + 2b + 2c + 2d + 2e = 110 Divide through by 2 .
a + b + c + d + e = 55
+129850 (b + e) + 4 + ( b + d) + 6 + (a + c) + 5 + (a + d) + 8 + ( c + e) + 7 = 28
(b + e) + ( b + d) + (a + c) + (a + d) + ( c + e) + 30 = 28
(b + e) + ( b + d) + (a + c) + (a + d) + ( c + e) = -2
2 [ a + b + c + d + e] = -2 divide both sides by 2
a + b + c + d + e = -1
+9479 Here's another interpretation.
a + 1 + 4 + c = 28 → a + c = 23
a + 3 + 5 + d = 28 → a + d = 20
b + 4 + 2 + d = 28 → b + d = 22
b + 1 + 3 + e = 28 → b + e = 24
c + 2 + 5 + e = 28 → c + e = 21 Add all five of these equations together to get...
2a + 2b + 2c + 2d + 2e = 110 Divide through by 2 .
a + b + c + d + e = 55
