The secret lies in the physics of pressure. Pressure is force divided by area.
One nail concentrates all the force into a small area, which easily punctures the balloon.
But when a surface touches many nails, the force is distributed among them, and the pressure on each nail is greatly reduced.
Even if additional force is applied and the balloon is against the nails, it may not burst because the pressure is evenly distributed.
For example, a person walking on a board with nails will not be hurt because each nail exerts minimal pressure on his skin, unlike a single nail that would definitely pierce his leg.
However, if there is too much force or not enough nails, the balloon or person will still be injured.
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