The Keypad of Doom (Hunger Games themed)

Logic Level 3

Katniss, Gale and Peeta have been captured by President Snow. They are locked up in separate cells, which have the same 3-digit passcode that is President Snow's favorite number. Having defected, Peeta is offered a chance to escape by determining a 3 number code by asking several questions. Wanting to escape certain doom, Katniss & Gale eavesdrop on the conversation.

Peeta: How are these numbers arranged?
Snow: They are arranged in increasing order. Peeta: What is the product of these numbers?
Snow: The product is 36.
Peeta: What is the sum of these 3 numbers?
Snow: The sum is equal to your cell number.
Peeta: I still don't know the answer. How many times does the largest number appear?
Snow: The largest number appears exactly once.

At this point, Peeta is able to enter the passcode and escape the cell. Can you help Katniss & Gale find the 3 digit passcode?

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