BMAD Posted July 21, 2015 Report Share Posted July 21, 2015 If If a,b,c,d are natural numbers andand a > b > c > d > 0then show that a - b - c -d > c - d .... To the moderators, this text box does not show up on my Ipad. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 22, 2015 Author Report Share Posted July 22, 2015 Assume that a+b+c+d=40 Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted July 23, 2015 Report Share Posted July 23, 2015 The inequality is equivalent to a-b > 2c, which is clearly not always true. For example. let a = 12, b = 11, c = 9, d = 8. Then a-b-c-d = -16, which is smaller than c-d = 1. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 24, 2015 Author Report Share Posted July 24, 2015 Hidden ContentI realized that, which is why I added my second post. :-D Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted July 24, 2015 Report Share Posted July 24, 2015 Still, I did assume that a+b+c+d = 40. Indeed 12+11+9+8 = 40. My counterexample holds. 1 Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 24, 2015 Author Report Share Posted July 24, 2015 Ah. I see my mistake completely now. I will retell the puzzle with all the information this time. Quote Link to comment Share on other sites More sharing options...
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BMAD
If If a,b,c,d are natural numbers and
and a > b > c > d > 0
then show that a - b - c -d > c - d
.... To the moderators, this text box does not show up on my Ipad.
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