有5个标记为1到5的袋子。给定袋子中的所有硬币重量相同。一些袋子的硬币重量为10克，另一些袋子的硬币重量为11克。我分别从1到5包中分别选择1、2、4、8、16个硬币。它们的总重量为323克。那么，具有11克硬币的袋子的标签产品为___。
(A) 15
(B) 12
(C) 8
(D) 1答案： (B)
解释：
There are 5 bags numbered 1 to 5.
We don't know how many bags contain 10 gm and
11 gm coins.
We only know that the total weights of coins is 323.
Now the idea here is to get 3 in the place of total
sum's unit digit.
Mark no 1 bag as having 11 gm coins.
Mark no 2 bag as having 10 gm coins.
Mark no 3 bag as having 11 gm coins.
Mark no 4 bag as having 11 gm coins.
Mark no 5 bag as having 10 gm coins.
Note: The above marking is done after getting false
results for some different permutations, the permutations
which were giving 3 in the unit place of the total sum.
Now, we have picked 1, 2, 4, 8, 16 coins respectively
from bags 1 to 5.
Hence total sum coming from each bag from 1 to 5 is 11,
20, 44, 88, 160 gm respectively.
For the above combination we are getting 3 as unit digit
in sum.
Lets find out the total sum, it's 11 + 20 + 44 + 88 + 160 = 323.
So it's coming right.
Now 11 gm coins containing bags are 1, 3 and 4.
Hence, the product is : 1 x 3 x 4 = 12. 替代解决方案：
有一些袋子，分别装有重量分别为11g和10g的硬币。从袋子1,2,3,4,5中挑选出来的1,2,4,8,16硬币的总重量为323。
现在我们需要找到10g和11g硬币的总和为323g。
设x为重10g的硬币数量，y为重11g的硬币数量
因此10x + 11y = 323………1
现在我们现在选择的硬币总数为1 + 2 + 4 + 8 + 16 = 31。
因此，x + y = 31…………2
求解方程式1和2，我们得到x = 18，y = 13。
因此，袋2和5(2 + 16 = x = 18)的硬币为10克，袋1、3和4(1 + 4 + 8 = y = 13)的硬币的克为11g。
因此，具有11克硬币的袋子的标签乘积为1 x 3 x 4 = 12。这个问题的测验