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maths! maths!(20 points)
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In each of the following cryptarithmetics, each letter stands for a different number. Can you find the number represented by each letter?1. AB + BA = CBC A = ______ B = ______ C = ______2. PQR - RQP = RPQ P = ______ Q = ______ R = ______3. XYY + XY + YY = YYY X = ______ Y = ______ 顯示更多 In each of the following cryptarithmetics, each letter stands for a different number. Can you find the number represented by each letter? 1. AB + BA = CBC A = ______ B = ______ C = ______ 2. PQR - RQP = RPQ P = ______ Q = ______ R = ______ 3. XYY + XY + YY = YYY X = ______ Y = ______ 更新: Maths P.10
最佳解答:
1) AB + BA 小於 200 , 所以 C = 1十位 A + 十位 B 的尾數是 B ,易知個位 B+A 有進位 1 ,推得A必為 9 ,所以原式是 92 + 29 = 121. A = 9 B = 2 C = 1 2) : P 不為 0, 由十位 Q - 十位Q = 尾數 P 可知 Q 已經借位給個位數, 立刻可確定 P = 9, (例如 11 - 2 = 9 , 17 - 8 = 9 , 10 - 1 = 9) 由於 PQR 的 Q 已借位, 一定不夠再減 RQP 中的Q, 由此可知必要向 P 借位,借位後得 (P - 1) - R = R (9 - 1) - R = R, R = 4 立知Q = 5 ,所以原式是 『954 - 459 = 495』 P = 4 Q = 9 R = 5 3) 個位 Y + Y + Y = Y尾 , 只有Y = 5x55 + x5 + 55 = 555 x = 4 X = 4 Y = 5
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