You have a bag with 101 coins identical in appearance, but 50 of these coins are fake, and the other 51 coins are genuine.
You know that a fake coin has a different weight from a genuine coin. The difference is only 1 gram, but you don't know if the fake coins are heavier or lighter than the genuine coins.
You received a curious scale to measure the weight of these coins. This scale has two pans, and instead of compare weighs, this is a digital scale that will show to you the modulus of the difference between the weights in the two pans. For example, if a pan has 67 grams, and the other pan have 55, the scale will show to you or (the same value). Also, the scale only works if there are something in both pans.
The problem is:
If you take at random a coin from this bag, it is possible to know if this coin is fake or not, using the scale only 1 time to weigh the coins?