I need help!

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Hey fellow students!

I need some math help! Here's the deal...

A person decides to shake hands with 6 different people on a certain day. The next day, each of the 6 people shake hands with 6 different people. The process continues until every person in the US has shaken someone's hand. How many days will it take until everyone in the US has shaken hands once? Assume that once a person shakes hands with 6 different people, he or she does not shake hands again. Assume the pop of the US is 248,709,873.

consider carefully the following: on each day how many "new" people are shaking hands and how many people in total have shaken hands when the day is done?

I'm not a math whiz and am stumped... this isn't a raise to 6 powers problem, which I can easily do. Any good ideas?

I'd appreciate a formula for this so that I'd know how to work it.

Thanks! :eek:


738 Posts

I have no idea what the answer is but we did a similar experiement in Microbiology to demonstrate a pandemic and figure out who started it. The prof used baby powder to coat our hands and the guilty party was dusted with corn starch. After being sprayed with iodine we could clearly see who gave it to another.

i hope you get the answer to the math problem...it is not my favorite subject!



322 Posts

I can tell you how to figure it out, but I can't give you the answer since I don't have a scientific calculator around. It's a problem based on logarithms. You need to figure out 6 raised to what power will give you the given population.

^=raised power ln=natural log

6^x = 248, 709, 873

ln 6^x = ln 248,709,873

x ln 6 = ln 248,709,873

x = ln 248,709,873 / ln 6

enter in a scientific calculator the (ln 248,709,873) divided by (ln 6) to get your answer. Let me know what the answer is.


355 Posts

Thanks, Cynthiann,

I'll try that and let you know. I figured it out my hubby's way, but there definitely was not an easy formula for that... I just worked it out line by line.

I'll check out your way and post it tomorrow. thanks again!


355 Posts

Hey... I can't believe it, but my solution to the problem was used as the class example! I used my husband's long hand method but did not feel at all sure about it. Cynthiann... later I tried your method and did come out with the same solution... it would take 10.75 days, or near that, to shake every hand in the US.

I guess since it's a stats class he wanted to see it written out, so I'm glad I did that. Thanks for your help... who knew? My dh has only had regular math... no algebra or anything... but he has such a natural bent for figuring things out. Wish I did!

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