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德．梅齊裡亞克的砝碼問題The Weight Problem of Bachet de Meziriac
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題目： 一位商人有一個40磅的砝碼，由於跌落在地而 碎成4塊.後來，稱得每塊碎片的重量都是整磅數，而且可以用這4塊來稱從1至40磅之間的任意整數磅的重物。（亦即利用這四個基本的數，透過加法或減法表示1~40的組合數） 請問：這4塊砝碼碎片各重多少？（列出1~40的組合數。） How to solve this problem?? 更新: Rex Lui: How can you find the weight 4 poises?? 更新 2: How can you find the weight of 4 poises??
Poise = 1, 3, 9, 27 L means left hand side, R means right hand side, W = weight W = 1 : L = W, R = 1 W = 2 : L = W + 1 = 3, R = 3 W = 3 : L = W, R = 3 W = 4 : L = W, R = 1 + 3 W = 5 : L = W + 1 = 3, R = 9 W = 6 : L = W + 3, R = 9 W = 7 : L = W + 1 + 3 + 9 = 27, R = 27 W = 8 : L = W + 3 + 9 = 27, R = 27 W = 9 : L = W, R = 9 W = 10 : L = W, R = 1 + 9 = 10 W = 11 : L = W + 1 = 12, L = 3 + 9 = 12 W = 13 : L = W, R = 1 + 3 + 9 = 13 W = 14 : L = W + 1 + 3 + 9 = 27, R = 27 W = 15 : L = W + 3 + 9 = 27, R = 27 W = 16 : L = W + 3 + 9 = 28, R = 27 + 1 = 28 W = 17 : L = W + 1 + 9 = 27, R = 27 W = 18 : L = W + 9 = 27, R = 27 W = 19 : L = W + 9 = 28, R = 27 + 1 = 28 W = 20 : L = W + 1 + 9 = 30, L = 27 + 3 = 30 W = 21 : L = W + 9 = 30, L = 27 + 3 = 30 W = 22 : L = W + 9 = 31, L = 27 + 3 + 1 = 31 W = 23 : L = W + 3 + 1 = 27, L = 27 W = 24 : L = W + 3 = 27, L = 27 W = 25 : L = W + 3 = 28, L = 27 + 1 W = 26 : L = W + 1 = 27, R = 27 W = 27 : L = W, R = 27 W = 28 : L = W, R = 1 + 27 = 28 W = 29 : L = W + 1 = 30, R = 27 + 3 = 30 W = 30 : L = W, R = 27 + 3 = 30 W = 31 : L = W, R = 27 + 3 + 1 = 31 W = 32 : L = W + 3 + 1 = 36, R = 27 + 9 = 36 W = 33 : L = W + 3 = 36, R = 27 + 9 = 36 W = 34 : L = W + 3 = 37, R = 27 + 9 + 1 = 37 W = 35 : L = W + 1 = 36, R = 27 + 9 = 36 W = 36 : L = W, R = 27 + 9 = 36 W = 37 : L = W, R = 27 + 9 + 1 = 37 W = 38 : L = W + 1 = 39, R = 27 + 9 + 3 = 39 W = 39 : L = W, L = 27 + 9 + 3 = 39 W = 40 : L = W, L = 1 + 3 + 9 + 27 = 40 2008-02-17 20:40:23 補充： I just tried some combinations but am quite sure that one of the poises must be 1
其他解答:
德．梅齊裡亞克的砝碼問題The Weight Problem of Bachet de Meziriac
發問:
題目： 一位商人有一個40磅的砝碼，由於跌落在地而 碎成4塊.後來，稱得每塊碎片的重量都是整磅數，而且可以用這4塊來稱從1至40磅之間的任意整數磅的重物。（亦即利用這四個基本的數，透過加法或減法表示1~40的組合數） 請問：這4塊砝碼碎片各重多少？（列出1~40的組合數。） How to solve this problem?? 更新: Rex Lui: How can you find the weight 4 poises?? 更新 2: How can you find the weight of 4 poises??
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最佳解答:Poise = 1, 3, 9, 27 L means left hand side, R means right hand side, W = weight W = 1 : L = W, R = 1 W = 2 : L = W + 1 = 3, R = 3 W = 3 : L = W, R = 3 W = 4 : L = W, R = 1 + 3 W = 5 : L = W + 1 = 3, R = 9 W = 6 : L = W + 3, R = 9 W = 7 : L = W + 1 + 3 + 9 = 27, R = 27 W = 8 : L = W + 3 + 9 = 27, R = 27 W = 9 : L = W, R = 9 W = 10 : L = W, R = 1 + 9 = 10 W = 11 : L = W + 1 = 12, L = 3 + 9 = 12 W = 13 : L = W, R = 1 + 3 + 9 = 13 W = 14 : L = W + 1 + 3 + 9 = 27, R = 27 W = 15 : L = W + 3 + 9 = 27, R = 27 W = 16 : L = W + 3 + 9 = 28, R = 27 + 1 = 28 W = 17 : L = W + 1 + 9 = 27, R = 27 W = 18 : L = W + 9 = 27, R = 27 W = 19 : L = W + 9 = 28, R = 27 + 1 = 28 W = 20 : L = W + 1 + 9 = 30, L = 27 + 3 = 30 W = 21 : L = W + 9 = 30, L = 27 + 3 = 30 W = 22 : L = W + 9 = 31, L = 27 + 3 + 1 = 31 W = 23 : L = W + 3 + 1 = 27, L = 27 W = 24 : L = W + 3 = 27, L = 27 W = 25 : L = W + 3 = 28, L = 27 + 1 W = 26 : L = W + 1 = 27, R = 27 W = 27 : L = W, R = 27 W = 28 : L = W, R = 1 + 27 = 28 W = 29 : L = W + 1 = 30, R = 27 + 3 = 30 W = 30 : L = W, R = 27 + 3 = 30 W = 31 : L = W, R = 27 + 3 + 1 = 31 W = 32 : L = W + 3 + 1 = 36, R = 27 + 9 = 36 W = 33 : L = W + 3 = 36, R = 27 + 9 = 36 W = 34 : L = W + 3 = 37, R = 27 + 9 + 1 = 37 W = 35 : L = W + 1 = 36, R = 27 + 9 = 36 W = 36 : L = W, R = 27 + 9 = 36 W = 37 : L = W, R = 27 + 9 + 1 = 37 W = 38 : L = W + 1 = 39, R = 27 + 9 + 3 = 39 W = 39 : L = W, L = 27 + 9 + 3 = 39 W = 40 : L = W, L = 1 + 3 + 9 + 27 = 40 2008-02-17 20:40:23 補充： I just tried some combinations but am quite sure that one of the poises must be 1
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