puzzleup 2016

lugionline

随便找一个就找到100以内的，显然不是122，我猜 79

硬算看来是不行的，相当于一个1万多变量的0-1规划，10种颜色机器就算不动了

lugionline

找到长度是52的解，谁来验证一下，不知道有没有更小的

({0, 1, 2, 3, 4, 5},
{0, 1, 6, 7, 8, 9},
{0, 1, 10, 11, 12, 13},
{0, 1, 14, 15, 16, 17},
{2, 3, 6, 7, 10, 11},
{2, 3, 8, 9, 12, 13},
{2, 4, 6, 8, 14, 15},
{2, 4, 7, 9, 16, 17},
{2, 5, 10, 12, 14, 16},
{2, 5, 11, 13, 15, 17},
{3, 4, 10, 12, 15, 17},
{3, 4, 11, 13, 14, 16},
{3, 5, 6, 8, 16, 17},
{3, 5, 7, 9, 14, 15},
{4, 5, 6, 7, 12, 13},
{4, 5, 8, 9, 10, 11},
{6, 9, 10, 13, 14, 17},
{6, 9, 11, 12, 15, 16},
{7, 8, 10, 13, 15, 16},
{7, 8, 11, 12, 14, 17},
{0, 1, 2, 6, 12, 17},
{0, 1, 2, 7, 13, 14},
{0, 1, 2, 8, 11, 16},
{0, 1, 2, 9, 10, 15},
{0, 1, 3, 6, 13, 15},
{0, 1, 3, 7, 12, 16},
{0, 1, 3, 8, 10, 14},
{0, 1, 3, 9, 11, 17},
{0, 1, 4, 6, 10, 16},
{0, 1, 4, 7, 11, 15},
{0, 1, 4, 8, 13, 17},
{0, 1, 4, 9, 12, 14},
{0, 1, 5, 6, 11, 14},
{0, 1, 5, 7, 10, 17},
{0, 1, 5, 8, 12, 15},
{0, 1, 5, 9, 13, 16},
{2, 3, 6, 9, 14, 16},
{2, 3, 7, 8, 15, 17},
{2, 4, 10, 11, 14, 17},
{2, 4, 12, 13, 15, 16},
{2, 5, 6, 8, 10, 13},
{2, 5, 7, 9, 11, 12},
{3, 4, 6, 8, 11, 12},
{3, 4, 7, 9, 10, 13},
{3, 5, 10, 11, 15, 16},
{3, 5, 12, 13, 14, 17},
{4, 5, 6, 9, 15, 17},
{4, 5, 7, 8, 14, 16},
{6, 7, 10, 12, 14, 15},
{6, 7, 11, 13, 16, 17},
{8, 9, 10, 12, 16, 17},
{8, 9, 11, 13, 14, 15}}

〇〇

lugionline 发表于 2016-12-2 12:32
随便找一个就找到100以内的，显然不是122，我猜 79

硬算看来是不行的，相当于一个1万多变量的0-1规划，1 ...

mma都算不出来,看来真难

newkid

lugionline 发表于 2016-12-2 14:19
找到长度是52的解，谁来验证一下，不知道有没有更小的

({0, 1, 2, 3, 4, 5},

我自己也发现错误了，但是想不出头绪。
本来我是这么想的，假设函数是f(18,6,3)
那么，包含有18的就是：f(17,5,2)
在不含18的里面，包含17的是：f(16,5,2)
...
所以 f(18,6,3)=f(17,5,2)+f(16,5,2)+...+f(5,5,2)
但是这个公式从一开始就是错的，包含18的分组方法同时也覆盖了不含18的。

〇〇

公式对6个颜色的小题对吗

newkid

〇〇 发表于 2016-12-2 23:18
公式对6个颜色的小题对吗

不对，因为子集不是互斥的，不管大小。

〇〇

No: 20       December 07, 2016  



EXPRESSION

EXPRESSION

Using the 10 digits (0,1,2,3,4,5,6,7,8,9), four arithmetic operations ("+","-", "x", " /"), exponentiation ("^"), factorial ("!"), decimal point ("."), and one pair of parentheses exactly one time, form an expression with maximum possible result.

Example:
(2.3/1-0+4x65)^789!

Notes:

-Order of operations: 1.(Factorial), 2.(Exponent), 3.(Multiplication and Division), 4.(Addition and Subtraction). Expressions inside the parentheses should be evaluated first.
-The signs "+", and "-" can be used only for addition and subtraction operations (not for assigning positive or negative values to the numbers).
-The decimal point should be between two digits.
-Operations having undefined results (like division to zero) are not allowed.

表达式
用10个数字,加减乘除运算符,乘方,阶乘,小数点,一对括号能形成最大的数是几

〇〇

〇〇 发表于 2016-12-7 20:26
No: 20       December 07, 2016  

运算顺序优先级 阶乘 > 乘方>乘除>加减 括号里的先计算
+-只能作加减号,不能作正负号
小数点要在两数字之间
不允许非法操作,比如除以0

〇〇

mathematica不能直接算
In[3]:= (2.3/1-0+4*65)^789!

General:vfl: Overflow occurred in computation.

Out[3]= Overflow[]

newkid

大数阶乘可以算，最后要比较答案时用取对数来比较大小。