A Puzzle A Day: 2026-05-04

In the 'Champions League Qualifier', Team Nova's 'Momentum Score' is calculated after each of their initial matches. This score reflects their cumulative performance in a unique way. An observer recorded Team Nova's Momentum Score after their first four matches: After Match 1: 5 After Match 2: 12 After Match 3: 23 After Match 4: 38 If this pattern continues, what will Team Nova's Momentum Score be after Match 5?
Correct: 57
Let S(n) be Team Nova's Momentum Score after Match n. We are given the following scores: S(1) = 5 S(2) = 12 S(3) = 23 S(4) = 38 First, let's find the differences between consecutive scores: Difference (S(2) - S(1)): 12 - 5 = 7 Difference (S(3) - S(2)): 23 - 12 = 11 Difference (S(4) - S(3)): 38 - 23 = 15 Next, let's find the differences between these differences (second differences): Difference between 11 and 7: 11 - 7 = 4 Difference between 15 and 11: 15 - 11 = 4 Since the second differences are constant (4), this indicates a quadratic pattern. To find the score after Match 5, we continue this pattern: The next first difference should be 15 + 4 = 19. Therefore, Team Nova's Momentum Score after Match 5 will be S(4) + 19 = 38 + 19 = 57.
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