Daily Math Puzzle: 2026-09-11

8 — Let E represent the number of Emeralds stolen. According to the thief's note: - The number of Rubies (R) = E + 5 - The number of Sapphires (S) = 2E - The total number of jewels (T) = R + E + S Substitute the expressions for R and S into the total jewels equation: T = (E + 5) + E + (2E) T = 4E + 5 The note also states that the total number of jewels was fewer than 40: T < 40 So, 4E + 5 < 40 Subtract 5 from both sides: 4E < 35 Divide by 4: E < 35 / 4 E < 8.75 Since only whole jewels can be stolen, E must be a positive integer. The statement 'three distinct types of gems were stolen: Rubies, Emeralds, and Sapphires' implies that some quantity of each type was taken. Therefore, E cannot be 0 (if E=0, then S=0, meaning no Emeralds or Sapphires were stolen, which contradicts the premise that three types 'were stolen'). So, E must be at least 1. Thus, the possible whole number values for E are 1, 2, 3, 4, 5, 6, 7, and 8. For each of these values of E, there is a unique possible total number of jewels (T): - If E = 1, T = 4(1) + 5 = 9 - If E = 2, T = 4(2) + 5 = 13 - If E = 3, T = 4(3) + 5 = 17 - If E = 4, T = 4(4) + 5 = 21 - If E = 5, T = 4(5) + 5 = 25 - If E = 6, T = 4(6) + 5 = 29 - If E = 7, T = 4(7) + 5 = 33 - If E = 8, T = 4(8) + 5 = 37 There are 8 distinct possible total numbers of jewels (9, 13, 17, 21, 25, 29, 33, 37) that satisfy all the conditions. Therefore, the correct answer is 8.