Another nice puzzle from the NASA collection sent to me by Suman Saraf.
Four friends, Holly, Belle, Carol, and Nick, gather for May birthdays. Holly announces that she has a game before dinner. She hid gifts for each of her friends inside three separate boxes secured with padlocks. She challenges her friends to figure out the combination without consulting each other.
She provides the following information. All the padlocks have the same combination. The padlocks use 3 digits from 0 to 9. She also tells them that the sum of the three digits is equal to nine, and every digit is equal to or greater than the previous digit. Holly tells each of her friends one of the digits in the combination. She states, “I’ve given the first digit to Belle, the second digit to Carol, and the third digit to Nick.” The caveat is that the friends cannot share their numbers with each other or they will forfeit the gifts.
Then Holly gives her friends 30 minutes to open the padlocks while she watches and finishes dinner.
The three friends begin to think of the solution. One by one, they each try their hand at their padlock, but none of them opens the padlock. Seeing that no one has succeeded, suddenly Carol realizes she knows the answer, and successfully opens her box, revealing a new fitness tracker. Following this, Nick opens his padlock, revealing a new tablet; and Belle opens her box to find new pair of headphones.
Having watched this entire event unfold, can you determine the correct combination?
As always, please send your answers as comments within the blog (preferred), or send an e-mail to firstname.lastname@example.org. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.