A single lollipop costs 12 beuros.
一根棒棒糖售价 12 欧元。
A packet of two lollipops costs 20 beuros,
两支棒棒糖一包，售价 20 欧元。
A packet of four costs 32 beuros,
一包四只售价 32 欧元。
A packet of eight lollipops costs 48 beuros,
一包八个棒棒糖售价 48 欧元。
A box with sixteen lollipos in costs 64 beuros.
一盒装有十六根棒棒糖的售价为 64 欧元。
Question 问题
What is the minimum amount of money that we need to spend in order to buy 21 lollipops?
为了买 21 根棒棒糖，我们需要花费的最少金额是多少？
A.112
B.116
C.108
D. 96
Explanation 解释
Correct answer is 108 beuros. If a package with two lollipops costs 20 beuros, each of them costs 20 / 2 = 10. In a package of four, each costs 32 / 4 = 8, and so on. Since packages with more lollipops are cheaper than those with fewer, it is always better to take larger boxes than multiple smaller ones.
正确答案是 108 欧元。如果一包有两根棒棒糖的价格是 20 欧元，那么每根的价格就是 20/2 = 10 欧元。一包四根的，每根的价格是 32/4 = 8 欧元，以此类推。由于棒棒糖数量多的包装比数量少的包装便宜，所以总是选择大包装比选择多个小包装更划算。
The task thus requires to go from the largest box to the smallest box and select a box that contains at most as many lollipops as you still need. Since every box contains twice as many lollipops as the next smallest one, it cannot happen that you need to take two boxes of the same size. The larger box is always cheaper than two small boxes.
因此，任务要求从最大的盒子开始，依次到最小的盒子，选择一个盒子，其中的棒棒糖数量最多与你仍需的数量相同。由于每个盒子的棒棒糖数量都是下一个较小盒子的两倍，所以不可能需要拿两个相同大小的盒子。较大的盒子总是比两个较小的盒子更便宜。
The situation would be more complicated if the discount for larger packages is so large that it would make sense to buy more lollipops than you need, and give them away.
如果大包装的折扣非常大，以至于购买超出自己所需数量的棒棒糖并将其送人变得合算，那么情况就会复杂得多。
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