Daily Math Puzzle: 2026-10-21

31 — Let's first determine which students the first staff member counted. The first staff member counts students at these positions: 1st, 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th. There are 9 students in total counted by the first staff member. Now, the second staff member counts students who were *not* counted by the first, but who are standing *strictly between* any two of the previously counted students. Since the 1st student and the 40th student were both counted by the first staff member, all students not counted must necessarily be 'between' two counted students (e.g., the 2nd, 3rd, 4th students are between the 1st and 5th; the 39th student is between the 35th and 40th). Therefore, the second staff member counts all the students who were *not* counted by the first staff member. Total students - Students counted by first staff member = Students counted by second staff member. 40 - 9 = 31 students. Alternatively, you can sum the students in each 'gap': 1. Between the 1st and 5th student: Students 2, 3, 4 (3 students). 2. Between the 5th and 10th student: Students 6, 7, 8, 9 (4 students). 3. Between the 10th and 15th student: Students 11, 12, 13, 14 (4 students). 4. Between the 15th and 20th student: Students 16, 17, 18, 19 (4 students). 5. Between the 20th and 25th student: Students 21, 22, 23, 24 (4 students). 6. Between the 25th and 30th student: Students 26, 27, 28, 29 (4 students). 7. Between the 30th and 35th student: Students 31, 32, 33, 34 (4 students). 8. Between the 35th and 40th student: Students 36, 37, 38, 39 (4 students). Adding these up: 3 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 3 + (7 * 4) = 3 + 28 = 31 students.