Jasmine and Zachary hosted their annual New Year's Eve party at their mansion. Including the hosts, there
were 22 couples in all. During the evening, many people shook hands with one another. No one shook
anyone's hand more than once, no one shook their spouse's hand, and no one shook their own hand. At the end
of the night, Zachary asked everyone (including Jasmine) how many hands they had each shaken. Amazingly,
everyone gave him a different answer! What was Jasmine's answer?
HINT: The 43 people that answered Zachary each gave a different number between 0 and 42.
If Jasmine had answered 0, then one of the other 42 people must have answered 42. But that is not
possible because they couldn't have shaken Jasmine's hand (based on her answer of 0) And since no one
shook their spouse's hand or their own hand, none of the others could have answered 41. Similar logic
rules out the possibility that Jasmine answered 42.
ANSWER:
21.
EXPLANATION: The 43 people that answered Zachary each gave a different number between 0
and 42. If Jasmine had answered 0, then one of the other 42 people must have answered 42. But that is not
possible because they couldn't have shaken Jasmine's hand (based on her answer of 0). And since no one
shook their spouse's hand or their own hand, none of the others could have answered 41. If Jasmine had
answered 42, then one of the other 42 people must have answered 0. But that too is not possible because
Jasmine would have shaken everyone's hand (except her spouse's and her own) based on her answer of 42.
So someone other than Jasmine answered 42. Let's say her name was Sienna. We then know that the person
who answered 0 was Sienna's spouse! For anyone else to have answered 0 would mean that they didn't shake
Sienna's hand which wouldn't be possible (based on her answer of 42). Continuing with this example, we see
that Jasmine could not have answered 1 or 41 either. If Jasmine had answered 1, she must have shaken hands
with Sienna. But that is not possible, because then none of the others could have answered 41. If the only
person that shook Jasmine's hand was Sienna and Sienna's spouse did not shake any hands, none of the
others that answered could have shaken more than 40 hands. If Jasmine had answered 41, she would have
shaken hands with all the others except Sienna's spouse and her own spouse Zachary. But that is not
possible because then none of the others could have answered 1 since they would have all shaken hands with
both Sienna and Jasmine.
So someone other than Jasmine answered 41. Let's say her name was Petra. Petra shook hands with everyone
except Sienna's spouse and her own spouse. We would then know that the person who answered 1 was Petra's
spouse since all the others who answered must have shaken hands with at least Sienna and Petra.
Continuing with the earlier logic, Jasmine could not have answered 40 or 2, 39 or 3, etc. The only answer
Jasmine could have given (for all 43 people to have given Zachary a different answer) is 21. Notice
that each couple has 42 combined handshakes between them, meaning that Zachary also shook 21 hands.
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
