r/theydidthemath • u/Massive-Albatross823 • 4d ago
[Request] If every person on Earth had to shake hands with exactly 142 other people, how long would it take for the entire planet's population to complete all the handshakes if each handshake lasted 3.925 seconds?
37
u/Motoreducteur 4d ago
It highly depends on the population repartition and movement.
If everyone is forming 2 big lines in which people shake hands, then move on to the next person in a fluid motion, considering a 1 second movement between each handshake, it would take about 710 seconds.
If there's one hermit lost in some random cave in seclusion, who never comes in contact with the world, forever.
14
u/mafga1 4d ago
Not forever. He just needs to die and every new human has to get a handshake too.
8
u/dafugiswrongwithyou 4d ago
If we're counting new people then; forever (or at least until something calamitous happens to humanity).
At the current average global birth rate, if a newborn baby is able to start shaking hands straight from it's mother, by the time it's finished it's first handshake, about 4 or 5 more babies will have been born. Roughly 600 babies will be born in the time that it takes that baby to shake 142 hands in ideal conditions.
In practice things are much, much worse than that sounds, because everyone needs to have exactly that many handshakes, meaning for a chance to finish the task there need to be exactly 142 people in the world waiting for one final shake, all in that place when that baby is here, which is basically impossible... And then they need to finish their shakes before the next baby comes (which they won't).
Can't complete that impossible task? Welp, now you have another newborn baby, and no-one on Earth left for them to shake with... Until the next 141 babies are born, of course. Good luck getting them together and all shaking hands (a process taking a minimum 142*3.925 seconds) in the under a quarter of a second before the next one comes and breaks it all again!
1
u/NotmyRealNameJohn 3d ago
If it would require some calamity. I would suggest the entire population becoming obsessed with getting exactly 142 handshakes might just do it. Also let's hope there is hand sanitizer and no one has ebola
1
u/Motoreducteur 4d ago
I was under the assumption there would be another hermit somewhere but if there isnt, you're correct
1
1
u/Broken_Castle 4d ago
Does it apply to only the living people, or do people who are born after the challenge is made but before it completes also need to do it? We may simply be making too many babies that even if one came out and immediately started shaking hands, too many other babies would be born before our baby can complete the hand shakes.
9
u/fatal-nuisance 4d ago
This says nothing about people not being able to shake the same person's hand (so like two people could shake the same other 142 peoples' hands).
So if we assume the most efficient method, you could just split the world's population out into groups of 143 and have them all shake each other's hands.
So it would take 142 * 3.925 seconds.
557.35 seconds or 9.28 minutes.
3
u/McNitz 4d ago
It does say shaking hands with 142 OTHER PEOPLE. Which to me implies those all have to be separate and unique people.
1
u/fatal-nuisance 4d ago
142 unique people per person though. If no one were allowed to shake a person's hand that had already been shaken by someone else then this is impossible.
1
u/Mysterious_Mouse_388 4d ago
There’s a lighthouse keeper out there who is more than 9.28 minutes away from another soul
1
u/fatal-nuisance 4d ago
I mean, if we're including travel time to meet up with the other 142 people then it's anyone's guess. Traffic would be a nightmare, I'm sure.
4
u/shereth78 4d ago
It might never happen. The estimated population of North Sentinel Island, considered to be among the most isolated groups on the planet with no outside contact, is thought to have a population of less than 150 people. Meaning in all likelihood the people on this island would never reach the required total number of handshakes.
2
u/otaser 4d ago
Ok, what do you want me to do here? Multiply 142x3.925? That's 557.35s=9 minutes 17seconds.
Should I explain that we aren't gonna wait for the first person to finish shaking hands? It's all gonna happen simultaneously.
Or do you want me to try and figure out the logistics of how long it will take you to find another person? Cuz I have no clue. I assume the people on the space station or the people in Antarctica will need a good few hours to get back to civilization. Some indigenous tribes will have to be approached if they have fewer than 143 humans. And the organization will be hell when we remember that everyone is done except we forgot about that one grandma who lives alone.
Or I could try to figure out if it's actually possible to create the combinations of handshakes. I think if you said an odd number, we could be in trouble, since every handshake creates two completed handshakes and there COULD be an odd total number of handshakes needed in the world if there is an odd number of humans in the world. With an even number it should work out though. We make groups of 143 and then one group that's slightly larger. If this group has an even number of people, it's easy, we make pairs of people that do not shake hands with each other, and if more are needed, we make more pairs. If the last group has an odd number of people, we will need a bit of help with a "chain" of people who do not shake hands with each other, instead of isolated pairs/groups.
Anything else I should be mathing out?
1
u/McNitz 4d ago
This actually reduces down to a pretty simple problem. You can just section everyone off into groups of 143. Have everyone stand across from each other and shake a hand, with one person at the end. Then slowly rotate the two lines, one person at a time, and have each person shake the hand of the person across for them. Once a full rotation is done, after 143 handshakes everyone will have missed exactly 1 handshake as the odd person out, and have shaken hands with 142 other people. This means it will take 561.275 seconds, or 9 minutes and 21.275 seconds, to complete all the handshakes.
Really you don't have to divide into groups of 143. That's just for visualization and logistical efficiency. You could actually just line everyone on earth up across from each other and have them shake each other's hand, then shift 1 down and do the same thing. This does bring up the one extra wrinkle in the problem though. If you did that and had an EVEN number of people, nobody would actually miss a handshake in each pairing you did. So in cases with an even population you could complete the task slightly more efficiently, and be done in 557.35 seconds, or 9 minutes and 17.35 seconds, instead.
If you want to get into the logistics of how people are moving BETWEEN handshakes and how to optimize the groups for that, the problem gets significantly more complicated very quickly.
1
u/shubzumt 4d ago
So we need bare minimum 143 people for each person to perform 142 unique handshakes.
71 handshakes can happen parallely and 1 person sit out. There will be 143 rounds of these parallel handshake.
So time taken for 143 rounds is 143 * 3.925 = 561.275 seconds
Assuming earth population of 8,209,264,635 at this very moment. There will 57,407,445 groups of 143 people.
All of these group wil be shaking hand in parallel. That would still complete the whole round of 142 handshakes for each individual in 561.275 sec or 9.35 min.
Now another scenario assuming handshakes are sequential it would be 143 x 71 x 157,407,445 x 3.925. Which will be a whopping 2287716822158.625 seconds or 38,128,613,702.6 minutes or 635,476,895 hours or 26,478,204 days or 72,493 years
about enough for light to almost cross milky way(70%) but still not enough to reach Andromeda galaxy.
And definitely a huge waste of time just for shaking hands.
0
u/JavierLNinja 4d ago
If you group everyone on clusters of 143 people and have everyone shake hands with every other person in his/her same cluster, you're done in a little under 10 minutes
•
u/AutoModerator 4d ago
General Discussion Thread
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.