# Ignorant Grand Piano Movers

A pianist who owns a rare antique four-legged piano hires a professional piano moving company to have it moved into his studio. After they've moved the piano, the movers present him with a bill based on the weight of the piano, which they say is $$900$$ pounds. When asked by the pianist how they came to that figure, they explain their procedure for grand pianos which usually have three legs:



1. Lift up one leg slightly and slide a weighing scale underneath.
2. Record down the weight on the scale.
3. Repeat this for all the other legs.
4. Sum up the weights.

The movers show him a diagram of the piano, and the weights recorded at each of the legs.

They conclude that this piano weighs $$200+200+200+300=900$$ pounds.

The pianist objects, saying that there is no way that piano can weigh $$900$$ pounds. He suspects that the back legs are double-counted, and insists that the piano only weighs $$200 + 200 + 300 = 700$$ pounds.

As it turns out, neither of them are right. What is the true weight of the piano, in pounds?

Note: The scale is not paper-thin, it does lift the piano leg a little off the floor.

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