6个球

fzy

难度：++

有6个一样大小的球，红色，绿色，蓝色各两个。每种颜色的两个球都是一个15克，一个16克。用一座无砝码，无刻度的天平称两次，能不能找出3个重球？

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fzy

Both solutions are correct, but I like the second one better, because it is a minimal solution: the second time there is only one ball on each side. www.ddhw.com

野 菜 花

Let the 6 balls be H, H', G, G', B, B'. 1st weigh: H+G and H'+B      if H+G>H'+B          2nd weigh: G and B':            if G>B': H,G,B heavier            if G=B': H, G, B' heavierwww.ddhw.com            if G     If H+G=H'+B           2nd weigh: H and H'               if H>H': H, G',B heavier               if H     If H+Gwww.ddhw.com

sean9991

Let the balls be R1, R2, G1, G2, B1, and B2. First, test R1, G1 against R2, B1.  There are two cases:www.ddhw.com 1.      Balanced, each group consists of 1 heavy and 1 light ball.  Then test G1 against G2.  WLOG, if G1 > G2, then R1 < R2, B1 < B2.www.ddhw.com 2.      WLOG, assume R1 + G1 > R2 + B1, therefore R1 > R2 and G1 >= B1.  Then test B1, G1 against B2, R2.  Three sub-cases:www.ddhw.com a.       B1 + G1 = B2 + R2.  Then B1 < B2, G1 > G2.www.ddhw.com b.      B1 + G1 < B2 + R2. Then B1 < B2, G1 < G2. c.       B1 + G1 > B2 + R2. Then B1 > B2, G1 > G2. www.ddhw.com