Video narration
For 3, 4, and 5, check 3 + 4 > 5. Since 7 is greater than 5, the sticks can close into a triangle. Now test 2, 3, and 5. Here, 2 + 3 = 5. The sticks line up exactly from end to end: a straight line, not a triangle. With 2, 3, and 6, 2 + 3 < 6. They cannot reach around it at all. So whenever you have three positive lengths, find the longest and add the other two. If the sum is greater, they form a triangle; if equal, they flatten into a line; if less, no triangle. So, can any three lengths make one? No. Three lengths make a triangle only when the sum of any two is greater than the third.