麦乐鸡块数是一个正整数,它可以通过将麦当劳®麦乐鸡块TM(在食用前)的份数相加得到,最初麦乐鸡块以 6、9 和 20 块装的盒子出售 (Vardi 1991, pp. 19-20 和 233-234; Wah and Picciotto 1994, p. 186)。除了 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37 和 43 之外,所有整数都是麦乐鸡块数。因此,数值 43 对应于 Frobenius 数 of
。
由于现在可以单独购买快乐儿童餐TM尺寸的鸡块盒(每盒 4 块),现代麦乐鸡块数是 4、6、9 和 20 的线性组合。这些新式的数字远不如以前有趣,只有 1、2、3、5、7 和 11 仍然是非麦乐鸡块数。因此,数值 11 对应于 Frobenius 数 of
。
贪婪算法可以用来找到给定整数
的麦乐鸡块展开式。这也可以在 Wolfram Language 中使用FrobeniusSolve[
6, 9, 20
, n]。下表总结了小整数的(经典)麦乐鸡块展开式。
![n](/images/equations/McNuggetNumber/Inline6.svg) | 麦乐鸡块展开式 |
6 | ![{](/images/equations/McNuggetNumber/Inline7.svg) 1,0,0![}](/images/equations/McNuggetNumber/Inline9.svg) ![}](/images/equations/McNuggetNumber/Inline10.svg) |
9 | ![{](/images/equations/McNuggetNumber/Inline11.svg) 0,1,0![}](/images/equations/McNuggetNumber/Inline13.svg) ![}](/images/equations/McNuggetNumber/Inline14.svg) |
12 | ![{](/images/equations/McNuggetNumber/Inline15.svg) 2,0,0![}](/images/equations/McNuggetNumber/Inline17.svg) ![}](/images/equations/McNuggetNumber/Inline18.svg) |
15 | ![{](/images/equations/McNuggetNumber/Inline19.svg) 1,1,0![}](/images/equations/McNuggetNumber/Inline21.svg) ![}](/images/equations/McNuggetNumber/Inline22.svg) |
18 | ![{](/images/equations/McNuggetNumber/Inline23.svg) 0,2,0 , 3,0,0![}](/images/equations/McNuggetNumber/Inline27.svg) ![}](/images/equations/McNuggetNumber/Inline28.svg) |
20 | ![{](/images/equations/McNuggetNumber/Inline29.svg) 0,0,1![}](/images/equations/McNuggetNumber/Inline31.svg) ![}](/images/equations/McNuggetNumber/Inline32.svg) |
21 | ![{](/images/equations/McNuggetNumber/Inline33.svg) 2,1,0![}](/images/equations/McNuggetNumber/Inline35.svg) ![}](/images/equations/McNuggetNumber/Inline36.svg) |
24 | ![{](/images/equations/McNuggetNumber/Inline37.svg) 1,2,0 , 4,0,0![}](/images/equations/McNuggetNumber/Inline41.svg) ![}](/images/equations/McNuggetNumber/Inline42.svg) |
26 | ![{](/images/equations/McNuggetNumber/Inline43.svg) 1,0,1![}](/images/equations/McNuggetNumber/Inline45.svg) ![}](/images/equations/McNuggetNumber/Inline46.svg) |
27 | ![{](/images/equations/McNuggetNumber/Inline47.svg) 0,3,0 , 3,1,0![}](/images/equations/McNuggetNumber/Inline51.svg) ![}](/images/equations/McNuggetNumber/Inline52.svg) |
29 | ![{](/images/equations/McNuggetNumber/Inline53.svg) 0,1,1![}](/images/equations/McNuggetNumber/Inline55.svg) ![}](/images/equations/McNuggetNumber/Inline56.svg) |
30 | ![{](/images/equations/McNuggetNumber/Inline57.svg) 2,2,0 , 5,0,0![}](/images/equations/McNuggetNumber/Inline61.svg) ![}](/images/equations/McNuggetNumber/Inline62.svg) |
另请参阅
找零问题,
完全序列,
Frobenius 数,
贪婪算法,
邮票问题
使用 Wolfram|Alpha 探索
参考文献
Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 19-20 and 233-234, 1991.
Wagon, S. "Greedy Coins." http://library.wolfram.com/infocenter/MathSource/5187/.Wah, A. and Picciotto, H. Lesson 5.8, Problem 1 in Algebra Themes, Tools and Concepts. Mountain View, CA: Creative Publications, p. 186, 1994.Wilson, D. rec.puzzles newsgroup posting, March 20, 1990.在 Wolfram|Alpha 中被引用
麦乐鸡块数
引用为
Weisstein, Eric W. "麦乐鸡块数。" 来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/McNuggetNumber.html
主题分类