数学令人难以置信,非常令人困惑的可能的新数学突破

发布于 2024-10-09 16:48:00 字数 1459 浏览 3 评论 0原文

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新人笑 2024-10-16 16:48:00

job1 为 job1 的数量,job2 为 job2 的数量。我们剩下两个方程和两个未知数:

job1 * 32 + job2 * 10 = 2566
job1 * 72 + job2 * 14 = 4835

因此:

job1 = 45.683...
job2 = 110.411...

给定 job1 作为较高的 xp/point 比率,并且您想要超过 4835 xp,将 job1 向上舍入,计算 job2 并将其向下舍入。

job1 = 46

job1 * 32 + job2 * 10 = 2566
job2 = 109.4

job2 = 109

检查:

job1 * 32 + job2 * 10 = 2562 points
job1 * 72 + job2 * 14 = 4838 xp

完成。

两个未知数很难说是“新的数学突破”:)

Let job1 be the amount of job1 and job2 be the amount of job2. We are left with two equations and two unknowns:

job1 * 32 + job2 * 10 = 2566
job1 * 72 + job2 * 14 = 4835

So:

job1 = 45.683...
job2 = 110.411...

Given job1 as the higher xp/point ratio and you wanna go over 4835 xp, round job1 up, compute job2 and round it down.

job1 = 46

job1 * 32 + job2 * 10 = 2566
job2 = 109.4

job2 = 109

Check:

job1 * 32 + job2 * 10 = 2562 points
job1 * 72 + job2 * 14 = 4838 xp

Done.

Two unknowns is hardly a 'new mathematical breakthrough' :)

若水般的淡然安静女子 2024-10-16 16:48:00

我假设您希望获得尽可能多的“XP”,同时通过在两个“工作”中的每一个上“点击”整数次 {n1, n2} 来花费不超过 2566 个“点” ”。 Mathematica 中的答案如下:

In[8]:= Maximize[{72 n1 + 14 n2, n1 >= 0, n2 >= 0, 
  32 n1 + 10 n2 <= 2566}, {n1, n2}, Integers]

Out[8]= {5956, {n1 -> 80, n2 -> 0}}

或者,也许您需要恰好花费 2566 点?那么你能做的最好的就是:

In[9]:= Maximize[{72 n1 + 14 n2, n1 >= 0, n2 >= 0, 
  32 n1 + 10 n2 == 2566}, {n1, n2}, Integers]

Out[9]= {5714, {n1 -> 78, n2 -> 7}}

这是你想要的吗?

I assume you want to get as much "XP" as possible, while spending no more than 2566 "points" by "clicking" an integer number of times {n1, n2} on each of two "jobs". Here is the answer in Mathematica:

In[8]:= Maximize[{72 n1 + 14 n2, n1 >= 0, n2 >= 0, 
  32 n1 + 10 n2 <= 2566}, {n1, n2}, Integers]

Out[8]= {5956, {n1 -> 80, n2 -> 0}}

Or, maybe you need to spend exactly 2566 points? Then the best you can do is:

In[9]:= Maximize[{72 n1 + 14 n2, n1 >= 0, n2 >= 0, 
  32 n1 + 10 n2 == 2566}, {n1, n2}, Integers]

Out[9]= {5714, {n1 -> 78, n2 -> 7}}

Is this what you wanted?

生生不灭 2024-10-16 16:48:00

a 为作业 1 的编号,b 为作业 2 的编号。

XP = 72 a + 14 b
P = 32 a + 10 b

您似乎想要求解 ab,使得 XP <= 4835P <= 2566b 尽可能大。

72 a + 14 b <= 4835
32 a + 10 b <= 2566

a = 0时,b将是最大的,即

b <= 4835 ÷ 14, => b <= 345
b <= 2566 ÷ 10, => b <= 256 

由于b必须同时低于345和256,所以它必须低于256。

代回:

72 a + 14 × 256 <= 4835, => a <= ( 4835 - 14 × 256 ) ÷ 72, => a <= 17
32 a + 10 × 256 <= 2566, => a <= ( 2566 - 10 × 256 ) ÷ 32, => a <= 0

所以 a = 0,XP 为 2560,使用的点数为 3584。

或者,您可以求解两个不等式的最接近满足,

72 a + 14 b <= 4835                (1)
32 a + 10 b <= 2566                (2) 
b <= ( 2566 - 32 a ) ÷ 10          (3) rearrange 2
72 a <= 4835 - 1.4 ( 2566 - 32 a ) (4) subst 3 into 1
27.2 a <= 1242.6
a <= 45.68

因此选择 a = 45 作为最大整数解,给出 b = 112,XP 为 4808,使用的点数为 2560

对于其中任何一个,都不需要计算机编程;如果与两个作业相关的常量发生变化,则公式也会发生变化。

对于较难解决的示例,相关的数学领域称为线性规划

Let a be the number of Job 1 and b the number of Job 2.

XP = 72 a + 14 b
P = 32 a + 10 b

You appear to want to solve for a and b, such that XP <= 4835, P <= 2566 and b is as large as possible.

72 a + 14 b <= 4835
32 a + 10 b <= 2566

b will be largest when a = 0, i.e.

b <= 4835 ÷ 14, => b <= 345
b <= 2566 ÷ 10, => b <= 256 

As b must be both below 345 and 256, it must be below 256.

Substitute back in:

72 a + 14 × 256 <= 4835, => a <= ( 4835 - 14 × 256 ) ÷ 72, => a <= 17
32 a + 10 × 256 <= 2566, => a <= ( 2566 - 10 × 256 ) ÷ 32, => a <= 0

so a = 0, XP is 2560 and points used is 3584.

Alternatively, you can solve for the closest satisfaction of the two inequalities

72 a + 14 b <= 4835                (1)
32 a + 10 b <= 2566                (2) 
b <= ( 2566 - 32 a ) ÷ 10          (3) rearrange 2
72 a <= 4835 - 1.4 ( 2566 - 32 a ) (4) subst 3 into 1
27.2 a <= 1242.6
a <= 45.68

so choose a = 45 as the largest integer solution, giving b = 112, XP is 4808, points used is 2560

For either of these, there's no computer programming required; if the constants associated with the two jobs change, then the formulas change.

For harder to solve examples, the relevant area of mathematics is called linear programming

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