A Puzzle A Day: 2026-05-05

Correct: 52

Let S be the number of sunstones and M be the number of moonstones. We are given three conditions from the riddle: 1. "The number of sunstones is three times the number of moonstones, minus five." This translates to the equation: S = 3M - 5 2. "The total count of sunstones and moonstones combined is less than 75." This translates to the inequality: S + M < 75 3. "There are more than 10 moonstones." This translates to the inequality: M > 10 Our goal is to find the maximum possible number of sunstones (S). First, substitute the expression for S from condition (1) into condition (2): (3M - 5) + M < 75 Combine like terms: 4M - 5 < 75 Add 5 to both sides: 4M < 80 Divide by 4: M < 20 Now we have two critical inequalities for M: From condition (3): M > 10 From our derived inequality: M < 20 Combining these, we get the range for M: 10 < M < 20. Since M represents a number of stones, it must be an integer. The integers satisfying 10 < M < 20 are 11, 12, 13, ..., 19. To maximize the number of sunstones (S), we need to maximize M, because the equation S = 3M - 5 shows that S increases as M increases. The maximum integer value for M that satisfies 10 < M < 20 is M = 19. Finally, substitute M = 19 back into the equation for S: S = 3(19) - 5 S = 57 - 5 S = 52 Let's quickly verify all original conditions with S=52 and M=19: 1. Is S = 3M - 5? 52 = 3(19) - 5 ⇒ 52 = 57 - 5 ⇒ 52 = 52 (True) 2. Is S + M < 75? 52 + 19 < 75 ⇒ 71 < 75 (True) 3. Is M > 10? 19 > 10 (True) All conditions are met, and S=52 is the result of using the maximum possible integer M. Thus, the maximum possible number of sunstones is 52.