• 0

Question

Posted · Report post

The father told his son to make as many non-intersecting triangles with his eight coins.
And for every such triangle (3 centers) counted on the table he will pay 1 coin but take
all coins used to make those triangles . How many coins shall the boy win or lose?

0

Share this post


Link to post
Share on other sites

10 answers to this question

  • 0

Posted · Report post

I believe if the boy makes a wheel with 7 nodes and a center point, the boy can claim 7 coins and lose three....

unless we claim that after selecting coins the remaining coins either placed by the father or the originals placed by the boy are reexamined for new triangles?/

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

I believe if the boy makes a wheel with 7 nodes and a center point, the boy can claim 7 coins and lose three....

unless we claim that after selecting coins the remaining coins either placed by the father or the originals placed by the boy are reexamined for new triangles?/

No, the boy only lose a coin for making 7 and only the boy places all his coins

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

The boy can make 13 triangles with 8 coins, so he can win 5 coins.

post-9659-0-30501500-1374156108_thumb.pn

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

The boy can make 13 triangles with 8 coins, so he can win 5 coins.

attachicon.gif13 triangles.png

he can do much better than ten

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

The boy can make 13 triangles with 8 coins, so he can win 5 coins.

attachicon.gif13 triangles.png

This calls for a distinction (is there one?) between non-intersecting and non-overlapping.

Hmm, yeah, I guess there is. :duh:

TSLF, care to comment?

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

i was thinking that triangle intersection is overlapping of area.. line intersection is overlapping of point

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

Well, if overlapping is not allowed then...

11 is the max

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

Well, if overlapping is not allowed then...

11 is the max

Bingo! Flatlander solution gives 11.

o

o o o o o o

o

But he can do much better.

Remember the centers of identical coins are "above" the table.

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

Well, if overlapping is not allowed then...

11 is the max

Bingo! Flatlander solution gives 11.

o

o o o o o o

o

But he can do much better.

Remember the centers of identical coins are "above" the table.

So, we're solving for flat triangles formed by coins in 3d space?

Lay 4 coins on the table forming a triangle with the 4th coin in the center. Stack the remaining 4 coins on top of the center coin. If I didn't miss anything then this produces 27 non-overlapping triangles.

0

Share this post


Link to post
Share on other sites
  • 0

Posted · Report post

Good one!


post-53237-0-43246500-1374320348_thumb.j
A roof more but still can be improved because 3 for 1 means atleast winning 24 coin pays for 8 of his coins.
32 triangles is just what he made .

0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now

  • Recently Browsing   0 members

    No registered users viewing this page.