The Birthday Riddle

On a Saturday afternoon you and your family are celebrating the 72nd birthday of grandpa James. When grandpa James has received all his gifts, he clinks his glass to get everyone’s attention. “First of all, I would like to thank you all for coming and for giving these beautiful gifts. Now it is my turn to give something back to you guys.” In his hands he holds a chest with a 3-digit lock on it. “As you all know, my passion for mathematics is big and I would like to share that with you”. Everybody nods their head since the only thing he talks about is math. “In this box I have hidden money for the one who cracks the 3-digit lock first. However, you may only try once.” Billy, your cousin, then asks “How are we supposed to do that? There are a total of 1000 combinations possible for that lock!”  Your grandpa replies “I will give you three hints about the code, listen carefully. The digits of the 3-digit code are in ascending order. The product of the three digits equals my age and the sum of the three digits equals the amount of years I have been married to my lovely wife Clara.”

Just when he says the last clue, you curse in your head. You have no idea how long James and Clara have been married. You try to ask others if they know how long they have been together, but as competitive as everyone is nobody answers the question truthfully. You almost give up, when all of a sudden Billy asks “I do not think we can solve this with this information, could you give us another clue?” James immediately replies with “You are absolutely right, my bad. It is probably my age influencing my math. Alright, the third clue is: the last digit of the code is the greatest of them all.”

You jump in the air from excitement and you immediately walk towards the chest, fill in the 3-digit code and open it. The whole family looks amazed at how fast you opened the chest after hearing what grandpa just said. Especially, because you made clear to your family members that you did not know how long James and Clara have been married. What 3-digit code did you use to open the chest?

If you want your 3-digit code to be checked, send it to the Nekst-Online committee!