 Quote by Tik
But just like a ball bouncing off the wall, why can't the first ball in the cradle retain some energy and bounce back, passing on the remaining energy to the next ball, hence conserving energy?
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There are multiple solutions that conserve both momentum and energy. You need to consider the direction of forces and how the forces propagate through the balls. Real world experiments show that the ball does bounce back a very small amount (not sure if this happens with an idealized cradle). There's also the issue that the pack of balls is shifting back and forth, when results in some component of opposing force from the strings the balls are attached to. Here's a web site with a good explanation:
cradle.htm