Daily Math Puzzle: 2026-03-19

6 — Let the sum of the original 10 positive integers be S_10. Since their average is 15, we can write the equation: S_10 / 10 = 15. Solving for S_10, we get S_10 = 15 * 10 = 150. Let 'x' be the smallest integer on the list. When 'x' is removed, there are 9 integers remaining. Let the sum of these 9 remaining integers be S_9. The problem states that the average of these 9 integers is 16, so: S_9 / 9 = 16. Solving for S_9, we get S_9 = 16 * 9 = 144. The sum of the original 10 integers (S_10) is composed of the sum of the 9 remaining integers (S_9) plus the smallest integer that was removed (x). Therefore, we can set up the equation: S_10 = S_9 + x. Now, substitute the values we found for S_10 and S_9 into this equation: 150 = 144 + x To find x, subtract 144 from both sides: x = 150 - 144 x = 6. So, the smallest integer on the original list is 6.