The Keypad of Doom (Hunger Games themed)
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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1 solution
Katniss & Gale don't know Peeta's number, but still start anyways. There are 8 possible combos: (3,3,4), (1,6,6), (1,4,9), (1,2,18), (2,3,6),(2,2,9), (1,3,12), & (1,1,36). Added up, they make 10,13,14,21,11,13,16,& 38 respectively. Out of these only 2 of the sets have the same number: 13. If Peeta had any other hallway number, he would have escaped then & there. But no! He asked for the third clue. So which is right: 1,6,6, or 2,2,9? Since the third clue says the largest number appears only once, the correct answer is 2,2,9. When night falls, Katniss & Gale escape, join Peeta outside, & save Panem.