bonanova Posted March 12, 2009 Report Share Posted March 12, 2009 Tony Toynbee the toy maker is busy painting the sides of a set of children's building blocks. The blocks are of traditional cubic shape, and Toynbee has paint of five different colors. No two adjacent sides of a block may have the same color. No two blocks in a set may have the same color pattern. How many blocks are there in the largest set Tony can make? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 30 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 12, 2009 Author Report Share Posted March 12, 2009 tony can make infinity boxes if he tries hard enough ☺ According to the OP color schemes cannot be repeated. Please use spoilers - PM me if you need help. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 12, 2009 Author Report Share Posted March 12, 2009 new guess: 55 Yes. Gold star if you include the reasoning. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 12, 2009 Author Report Share Posted March 12, 2009 51 One way to use three colors. C(5,2)*C(3,2) ways to use four colors = 30 5 * C(4,3) ways to use all five colors = 20 Two out of three. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 Two out of three. There should be a smiley... Obviously more than one way to use three colors. More like C(5,3)=10, for a total of 60 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 5 blocks largest set possible. Each block has 6 areas( top,bottom,4 sides ) to paint. The first block gets the same color top and bottom and the 4 sides the other 4 colors, the 2nd block a different color top and bottom and the 4 sides the other 4 colors and so on. [spoiler='5 blocks is wrong. 2 colors on sides can be swaped before repeating pattern.']10 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 12, 2009 Author Report Share Posted March 12, 2009 There should be a smiley... Obviously more than one way to use three colors. More like C(5,3)=10, for a total of 60Should have said 1 out of 3. Rethink the 5 color case. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 so i get 54, 9 ways to use 3 colors, 30 ways to use 4 colors, and 15 ways to use 5 colors, Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 Should have said 1 out of 3. Rethink the 5 color case. [spoiler=Double !...]5*4*3=60, not 5*C(4,3)=20... for a total of, er, I think we're at 100 now. Trust me to screw up the two obvious cases... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 Yes. Gold star if you include the reasoning. Ok, so from the first page I showed that when you use all 5 colors there are 15 possibilites. 4 colors: When using 4 colors, 2 colors are repeated (5 choose 2=10). The other two colors are 3 choose 2 = 3. 10*3=30 3 colors: All 3 colors are repeated: 5 choose 3 = 10 Total: 15+30+10=55 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 well you get it from me voltage, for you made me see the one case i was failing to see! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 [spoiler=Double !...]5*4*3=60, not 5*C(4,3)=20... for a total of, er, I think we're at 100 now. Trust me to screw up the two obvious cases... I think that's a triple http://brainden.com/forum/uploads/emoticons/default_duh.gif' alt=':duh:'> now...15, not 60. Anyway, voltage has the answer and explanation... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 12, 2009 Report Share Posted March 12, 2009 Zero!!!!A cube has six sides! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 13, 2009 Author Report Share Posted March 13, 2009 Zero!!!!A cube has six sides! Uh ... no. But welcome to the Den - enjoy your time here. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 13, 2009 Author Report Share Posted March 13, 2009 Ok, so from the first page I showed that when you use all 5 colors there are 15 possibilites. 4 colors: When using 4 colors, 2 colors are repeated (5 choose 2=10). The other two colors are 3 choose 2 = 3. 10*3=30 3 colors: All 3 colors are repeated: 5 choose 3 = 10 Total: 15+30+10=55 As promised ... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 13, 2009 Report Share Posted March 13, 2009 There should be a smiley... I thought the same thing. How about this? Quote Link to comment Share on other sites More sharing options...
Question
bonanova
Tony Toynbee the toy maker is busy painting the sides of a set of children's building blocks.
The blocks are of traditional cubic shape, and Toynbee has paint of five different colors.
No two adjacent sides of a block may have the same color.
No two blocks in a set may have the same color pattern.
How many blocks are there in the largest set Tony can make?
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