James Tanton
Craig Dawson
@jamestanton @SofARMaths The number of reds in col 1, will always equal blues in col 2?
1-10 red, 11-20 blue. Arrange nmbrs in a 10x2 grid so that left col increases,right col decreases. What sure to be true about color pattern?
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@craig__fstr@SofARMaths True. And a bit more holds too. -
@jamestanton@SofARMaths Turn the grid by 180 degrees & the colours will switch, but the pattern will remain. R R B R will be B B R B? -
@craig__fstr@SofARMaths That's cool and true! (Hadn't thought about phrasing it that way!) Now .. why this the case?
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@jamestanton paired R/B in each row...? - View other replies
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@jamestanton or B/R - either way: one of each colour in each row... -
@SofARMaths Can you explain why?
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@jamestanton Because every n from 1-10 not in top left must be in bottom right and the numbers so placed will "fill" all ten "slots"... - View other replies
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@jamestanton i.e. consider placing 1st number x in top left. All numbers less than x must go at bottom right.. Next add y TL... -
@jamestanton makes sense? - View other replies
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@SofARMaths Sorry. Yes! I think you're thinking is right.
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@jamestanton and starting with 11 in TL is trivial? same as 1 with colours reversed? -
@jamestanton If there is a monochrome pair, there is another of a different color. http://www.cut-the-knot.org/Curriculum/Algebra/ItemParity2.shtml … This is a contradiction
John Rowland
Alexander Bogomolny
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