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The Dollar Bill

Question

Bill has five  pennies .  He shall make as many  triangles as he can to gain more money. For every unique triangle that he creates on a flat table (3 corners at centers of coins) he wins a nickle but for some triangles that dont overlap or intersect with other triangles, he wins a dime. He shall declare the triangles he formed on the table. So Bill can name the identical coins A,B,C,D and E. Note U$  penny  is 1-cent, nickle is 5-cents and dime is 10-cents.

How shall Bill put all his coins on the table for greatest earnings?

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2 answers to this question

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Total of  $ 0.70 ;  Arrange 4 pennies in a circle around a penny in the center  (A )  such that none of the  outside pennies are on the same diameter passing  thru (A)    Let's assume that as we look at our screen (B) is directly below (A) at a distance of the radius ;  Moving CW up to the left more than 90 deg is (C) ; continuing CW approx 70 degrees  which stops us short of being diametrically opposite (B) is location of (D) :  continue CW about 90 degrees for  (E).    You have 4 triangles which do NOT over lap  ABC;  ACD ; ADE ;  AEB .   You then have 6 triangles created by  lines from(B) to (D) and from (C) to (E)   These triangles being BCD ;  BDE;  BDA;  CDE ; CEA ; CEB.   So we have 4 @ 0.10 = $040  and 6 @ .05 = 0.30 for a total of $ 0.70

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