Math Homework Help for 8th Grader

Juniper · 03-18-2010, 08:22 PM

Got a problem to solve. I worked on this with my daughter last night, and I got an answer, but apparently I'm wrong!

There are six busybodies in town who like to share information. Whenever one of them calls another, they both know everything that the other one knew by the end of the conversation. One day, each of the six women picks up a juicy piece of gossip. What is the minimum number of phone calls required before all six of them know all six of these tidbits?

I got 10, but I guess it's not right!

Help?

Clodfobble · 03-18-2010, 09:42 PM

10's the best I got, sorry.

skysidhe · 03-18-2010, 09:45 PM

It's the worst problem ever. 5, no 3 no....oh I don't know.

Pie · 03-18-2010, 09:51 PM

I got nine.

ABC DEF

B calls A and C (2)
E calls D and F (2)

B calls E (1)

B calls A and C (2)
E calls D and F (2)

Total: 9

squirell nutkin · 03-18-2010, 10:15 PM

I think I got 8.

Each caller is a letter and each number is a bit of gossip.

A B C D E F
1 2 3 4 5 6

A calls F (A has 1,6 F has 1,6)
B calls E (B has 2,5 E has 2,5)
C calls D (C has 3,4 D has 3,4)
A calls E (A has 1,2,5,6 E has 1,2,5,6)
A calls D (A has 1,2,3,4,5,6 D has 1,2,3,4,5,6)
A calls B (A has 1,2,3,4,5,6 B has 1,2,3,4,5,6)
C calls E (C has 1,2,3,4,5,6 E has 1,2,3,4,5,6)
E calls F (E has 1,2,3,4,5,6 F has 1,2,3,4,5,6)

Juniper · 03-18-2010, 10:33 PM

I had amended my answer to 9 also, but I think Squirrel's right!

Thanks!

Every quarter daughter gets these "critical thinking" worksheets for math - things like the family crossing the river in a boat that can only hold two, the frogs and lily pads, various puzzles . . . and for us non-math types, they are HARD!!!

squirell nutkin · 03-18-2010, 11:31 PM

If a hen and a half can lay an egg and a half in a day and a half, how long does it take a cricket with a wooden leg to kick all the seeds from a dill pickle?

toranokaze · 03-19-2010, 01:33 AM

an infinite amount of time

squirell nutkin · 03-19-2010, 09:26 AM

You get partial Credit. It takes half as long as it takes for an elephant with a wooden leg to bore a hole in a bar of soap.

monster · 03-19-2010, 09:40 AM

Quote:

Originally Posted by Juniper

Got a problem to solve. I worked on this with my daughter last night, and I got an answer, but apparently I'm wrong!

There are six busybodies in town who like to share information. Whenever one of them calls another, they both know everything that the other one knew by the end of the conversation. One day, each of the six women picks up a juicy piece of gossip. What is the minimum number of phone calls required before all six of them know all six of these tidbits?

I got 10, but I guess it's not right!

Help?

Why don't they conference call? Then it's 5 calls, right?

Flint · 03-19-2010, 10:48 AM

No two card shuffles will ever be the same.

monster · 03-19-2010, 11:01 AM

but strangely, two flint posts can be, despite the fact that the number of possible word/idea combinations in that head must outstrip the number of possible card shuffles.

squirell nutkin · 03-19-2010, 01:01 PM

Quote:

Originally Posted by Flint

No two card shuffles will ever be the same.

No, but eight will.

See it:

Pie · 03-19-2010, 01:22 PM

Mathematical closed form solution: in this example, k=2, n=6.
f(n,k)=2[(n−k)(k−1)] =2[(4)(1)] = 8

Squirrel for the win!
ETA, Juni, this is neither a trivial or a simple problem. Kudos to your kid's math teacher!

Pie · 03-19-2010, 01:34 PM

Interesting that ONR is supporting this research. Network topology is still a hot topic!

03-18-2010, 08:22 PM	#1
Juniper I know, right? Join Date: Aug 2008 Posts: 1,539	Math Homework Help for 8th Grader Got a problem to solve. I worked on this with my daughter last night, and I got an answer, but apparently I'm wrong! There are six busybodies in town who like to share information. Whenever one of them calls another, they both know everything that the other one knew by the end of the conversation. One day, each of the six women picks up a juicy piece of gossip. What is the minimum number of phone calls required before all six of them know all six of these tidbits? I got 10, but I guess it's not right! Help?

03-18-2010, 09:42 PM	#2
Clodfobble UNDER CONDITIONAL MITIGATION Join Date: Mar 2004 Location: Austin, TX Posts: 20,012	10's the best I got, sorry. __________________ My book My other book My spirit animal

03-18-2010, 09:51 PM	#4
Pie Gone and done Join Date: Sep 2001 Posts: 4,808	I got nine. ABC DEF B calls A and C (2) E calls D and F (2) B calls E (1) B calls A and C (2) E calls D and F (2) Total: 9 __________________ per·son \ˈpər-sən\ (noun) - an ephemeral collection of small, irrational decisions The fun thing about evolution (and science in general) is that it happens whether you believe in it or not.

03-18-2010, 10:15 PM	#5
squirell nutkin has a second hand user title Join Date: Feb 2006 Location: in a Nut House Posts: 2,017	I think I got 8. Each caller is a letter and each number is a bit of gossip. A B C D E F 1 2 3 4 5 6 A calls F (A has 1,6 F has 1,6) B calls E (B has 2,5 E has 2,5) C calls D (C has 3,4 D has 3,4) A calls E (A has 1,2,5,6 E has 1,2,5,6) A calls D (A has 1,2,3,4,5,6 D has 1,2,3,4,5,6) A calls B (A has 1,2,3,4,5,6 B has 1,2,3,4,5,6) C calls E (C has 1,2,3,4,5,6 E has 1,2,3,4,5,6) E calls F (E has 1,2,3,4,5,6 F has 1,2,3,4,5,6) __________________ And now I'm finished posting.

03-18-2010, 11:31 PM	#7
squirell nutkin has a second hand user title Join Date: Feb 2006 Location: in a Nut House Posts: 2,017	If a hen and a half can lay an egg and a half in a day and a half, how long does it take a cricket with a wooden leg to kick all the seeds from a dill pickle? __________________ And now I'm finished posting.

03-18-2010, 09:45 PM	#3
skysidhe ~~Life is either a daring adventure or nothing.~~ Join Date: Apr 2006 Posts: 6,828	It's the worst problem ever. 5, no 3 no....oh I don't know.

03-18-2010, 10:33 PM	#6
Juniper I know, right? Join Date: Aug 2008 Posts: 1,539	I had amended my answer to 9 also, but I think Squirrel's right! Thanks! Every quarter daughter gets these "critical thinking" worksheets for math - things like the family crossing the river in a boat that can only hold two, the frogs and lily pads, various puzzles . . . and for us non-math types, they are HARD!!!

03-19-2010, 01:33 AM	#8
toranokaze I'm still a jerk Join Date: Oct 2007 Location: Little Mexico Posts: 1,817	an infinite amount of time __________________ "Without deviation from the norm progress is not possible." - Frank Zappa It is the ignorance of ignorance that lead to the death of knowledge The Virgin Mary does not weep for her son, for he is in paradise. She weeps for the world , for we are in suffering.

03-19-2010, 09:26 AM	#9
squirell nutkin has a second hand user title Join Date: Feb 2006 Location: in a Nut House Posts: 2,017	You get partial Credit. It takes half as long as it takes for an elephant with a wooden leg to bore a hole in a bar of soap. __________________ And now I'm finished posting.

03-19-2010, 10:48 AM	#11
Flint Snowflake Join Date: Mar 2006 Location: Dystopia Posts: 13,136	No two card shuffles will ever be the same. __________________ **************** There's a level of facility that everyone needs to accomplish, and from there it's a matter of deciding for yourself how important ultra-facility is to your expression. ... I found, like Joseph Campbell said, if you just follow whatever gives you a little joy or excitement or awe, then you're on the right track. . . . . . . . . . . . . . . . . . . . . . . . . . . Terry Bozzio**

03-19-2010, 11:01 AM	#12
monster I hear them call the tide Join Date: Dec 2005 Location: Perpetual Chaos Posts: 30,852	but strangely, two flint posts can be, despite the fact that the number of possible word/idea combinations in that head must outstrip the number of possible card shuffles. __________________ The most difficult thing is the decision to act, the rest is merely tenacity Amelia Earhart

03-19-2010, 01:22 PM	#14
Pie Gone and done Join Date: Sep 2001 Posts: 4,808	Mathematical closed form solution: in this example, k=2, n=6. f(n,k)=2[(n−k)(k−1)] =2[(4)(1)] = 8 Squirrel for the win! ETA, Juni, this is neither a trivial or a simple problem. Kudos to your kid's math teacher! Attached Images __________________ per·son \ˈpər-sən\ (noun) - an ephemeral collection of small, irrational decisions The fun thing about evolution (and science in general) is that it happens whether you believe in it or not.

03-19-2010, 01:34 PM	#15
Pie Gone and done Join Date: Sep 2001 Posts: 4,808	Interesting that ONR is supporting this research. Network topology is still a hot topic! __________________ per·son \ˈpər-sən\ (noun) - an ephemeral collection of small, irrational decisions The fun thing about evolution (and science in general) is that it happens whether you believe in it or not.

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