I am a manager of a coin casting foundry. We produce perfectly round coins with some (fixed) thickness and a diameter of exactly 1 inch. The working room is well-secured such that if any coin tries to leave the room, the alarm goes off. To allow workers to safely carry coins out of the room, a special container that is 10" * 10" square is available. A maximum of 1 layer of coins may be spread in the container and when it passes the door, the alarm won't go off. Normally, up to 100 coins can be carried with one such container.
Yesterday we encountered a theft. A container (with coins) was taken out of the working room without triggering the alarm. But what confused me is that 106 coins were lost. I don't know how the thief took the extra 6 coins without setting off the alarm.
Can you help me solve this mystery?