maths! maths!(20 points)

meilk豆腐貓

2010-07-24 7:51 pm

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1:

Maths P.10

回答 (1)

用戶2053

2010-07-24 8:05 pm

✔ 最佳答案

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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