Take out N gems from the boxes numbered N, n= 1, 2, 3, 4.

These 10 jewels are marked according to the box number.

Then put this 10 gem into the balance and weigh it together.

If it is 100g, the fifth box is a fake.

If it is 90g, 1 box is a fake.

If it is 80 grams, the second box is fake.

If it is 70 grams, the third box is a fake.

If it is 60 grams, the fourth box is fake.