Party Puzzle: Newsletter Challenge (December 2020)

42.

Overheard Vogon Conversation at the Party...

Now that we know the "question" we will no longer need "Deep Thought" and we will not even need the "Earth." Now we know where to put our hyperspace bypass.

_____________

thewildotter

Elaine's answer is that "It is not possible".

You have 42 people besides Mike and Elaine. Each of these can shake hands with up to 42 people and each shakes hands with a different number. Number them by number of handshakes. Assume we do these in order.

#1 shakes with one of 42 people and leaves the room, leaving 41 people. #1 can't shake hands anymore.

#2 shakes with two of 41 people and leaves the room, leaving 40 people.

#3 shakes with three of 40 people and leaves the room, leaving 39 people.

...

#21 shakes with 21 of 21 people and leaves the room, leaving 20 people.

#22 doesn't have enough people to shake hands with, and so on with the rest.

Withdraw previous answer, it's a little more complicated...

None....she's a hugger....

1, 2, break...

Elaine shook hands with 21 people.

******* Spoiler alert ********

https://mindyourdecisions.com/blog/2017/08/06/the-impossible-handshake-logic-puzzle-a-martin-gardner-classic/#:~:text=Answer%20To%20Seemingly%20Impossible%20Handshake%20Logic%20Puzzle&text=and%20Mrs.,%2C%201%2C%20or%202%20people.

Elaine's answer could be anything from 1 to 42, because :

1. not everyone shook everyone's hand.

2. Elaine never shook her spouses hand.

No one can shake their own hand.

The annual new year's eve party could of been at a city park, so there wouldn't be a room to leave from and had it been at a house why would you leave the room if that is where the party is at ?

Shake hand's formally or the two handed sheila (womans) version?

So anywhere from zero to 84 unless someone had lost two hands as the reult of an accident or other means.
To many imponderables in the question.

If the couple are Mike Nichols and Elaine May, all bets are off.

Not enough information to calculate an answer. There were 22 couples but no information on how many of the couples were married and therefore had a spouse. Or were married but had brought some other person's spouse to the party. The question does not preclude unmarried couples from shaking each others hands.

First notice that the 43 people questioned have to answer all possible 43 numbers from 0 to 42, and, that Mike must share his "score" with one of the other revellers but that we are not interested in his score.

Start with guest Forty Two and note that they shake hands with everyone including the hosts but excluding their own spouse, who must therefore become guest Zero.

Now moving to guest Forty One: they have to shake hands with everyone except Zero and their own spouse. At this point everyone has a score of 2 or more except Zero and Forty One's spouse who must therefore become guest One.

Carrying on

Forty and spouse Two

Thirty Nine and Spouse Three

.

.

Twenty Two and spouse Twenty

At this point you just need to count the number of times Elaine has shaken hands to confirm that it's the only number left.

Well: she shook hands with

Forty Two

Forty One

.

.

.

And Twenty Two

21 (That's a relief. Incidentally the same 21 that Mike shook hands with.)

Personally: when I'm at a new years eve party, after the first 5 (±2) glasses of scotch I can't even remember the number of the year we're about to enter. So how on earth all 43 of these people remembered how many hands they shook is a much bigger puzzle.

For some reason I looked at it as a social problem rather than a mathematical one and was totally confused at first.

Obviously they are not following CDC guidance, which means hat they are not following other arbitrary guidance and the answer is indeterminate as inevitably someone will shake hands again. Also there is no mention of hand sanitizer or gloves, the gloves being totally irrelevant to contact spread.

At the current time for RESPONSIBLE mind numbed robots is four or less since you aren't supposed to have more than six individuals from two households unless you count the arresting officer sent to enforce the limit because your neighbor ratted you out.

Mike and Elaine welcome the 42 guests, and she shakes each hand. Having done so, nobody else can achieve that number because she is eliminated as a possible hand-shaker for all. I'll run with 42 as an answer, but it's linguistically slippery. Mike did not ask/answer the question of himself, which could have resulted in '42' as an answer.

Yes, it makes sense that the hosts have shaken hands with everybody else but in this case Mike cannot get 43 different answers (from 0 to 42) because there is nobody with 0 handshakes. Instead, he will get two ‘21’ answers – just follow the logic of my #11.

The same with your #18 – the only way Mike can get 43 different answers is if he and Elaine are the couple with 21 handshakes each.

Reading again, I think you are correct. Mike still needs a good telling off, and I'll look to see if it could be argued that the published answer is wrong - that's half the fun. I don't recall any Challenge Questions that needed an edit to the 'official' answer, but many have generated good discussion about the answer.

Update to previous answer:

I'm resisting looking at the spoiler, but have nearly convinced myself to go the other way and suggest 0 or 1. Mike and Elaine could both answer '42', but with 42 possible greetings (44 people minus self and spouce) the only other unique answer is '0'. I'd just slap Mike and ask where the hand sanitizer was.

"Check back later this month for the answer, right here on CR4."

Although I think the answer been given, it would be great to see the officially worded explanation. Fingers crossed that the partygoers are all well.

"Check back later this month for the answer, right here on CR4."

I know it's tough times, but please post an official answer. I keep waking at night worried about this. UK rules completely stop this type of party, but please give the answer. My taking a bath to chill could have horrible results.

Alex Roman's reply at #11 is correct and well explained.

I agree, but the pedant in me likes to see the 'official' answer. There have been previous questions where the given answer has provoked much debate, and it often contains good input - related to topic, but with alternative ways of explanation. That's not knocking the solution by Alex, just a general observation of how problems are solved and explained. As a small example, it took me years to realize I could expand (x + y)³ purely by observation of the form rather than the laborious route most often taught.

Is it just me......"Check back later this month for the answer, right here on CR4.".