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<EN>
If you are here directly, here is the link with the context: https://www.facebook.com/reel/375727531350653/
since the video is in Chinese,
here are the translations of the instructions given by GaoYuTian to get your age:
1) pick a number from 1 to 10
2) multiply it by 2, then add 5 to the result
3) take this result and multiply it by 50
4) if you had your birthday, add 1772 to the result, else, add 1771 to the result
5) subtract the year when you were born from the result
6) in this case, we will have an answer with 3 digits, the first digit is the number you have picked at the beginning, and the last two digits represent your age.
this blog post will explain why this method works
<中文>
如果你是直接来到这里的，原视频在这里
这一个帖文会讲解“为什么这个方法行得通”
Why does it work? / 为什么行得通?
let's say the number we have picked at the beginning is "t", we have the following table
假设我们选择的数字是 "t"，我们就可以获得以下表格：
Steps or Instructions \\ 步骤 | The result so far in Mathematical form \\ 目前为止 运算结果的数学表现式 |
pick a number from 1 to 10 \\ 1-10之间随便想一个数字 | t |
multiply it by 2, then add 5 to the result \\ 把你想的数字 乘于 2 然后 加5 | 2t + 5 |
take this result and multiply it by 50 \\ 用这个结果继续 乘于 50 | (2t + 5) * 50 |
if you had your birthday, add 1772 to the result, else, add 1771 to the result \\ 如果你的生日已经过了，请加上1772；如果你的生日还没过，请加上1771 | (2t + 5) * 50 + 1772 or (2t + 5) * 50 + 1771 |
subtract the year when you were born from the result \\ 然后减去你出生年份 | let "y" be the year of your birth, 设 "y" 为你的出生年份，(2t + 5) * 50 + 1772 - y or或 (2t + 5) * 50 + 1771 - y |
in this case, we will have an answer with 3 digits, the first digit is the number you have picked at the beginning, and the last two digits represent your age. \\ 最后我们会得到一个三位数，第一个数字就是你想的数字，后面两位就是你的年龄 | 1shelet "a" be your age, 设"a"为你的年龄， (2t + 5) * 50 + 1772 - y = 100t + a or (2t + 5) * 50 + 1771 - y = 100t + a |
so far we have 2 equations, let's focus on the one which considers that you had your birthday, which is :
目前为止我们有两个方程式，我们先正对如果你已将过了生日的情况:
(2t + 5) * 50 + 1772 - y = 100t + a
here we can try to rearrange the equation into something straightforward.
重新整理一下方程式，我们会获得:
(2t + 5) * 50 + 1772 - y = 100t + a
(100t + 250) + 1772 - y = 100t + a
as you can see the number you pick multiplied by 100 will be canceled on both sides, meaning whatever number you picked, it will never affect "your age".
what we have here now is :
由此可见你开始选择的数字乘于100 将会被抵消，
也就是说不管你选择什么数字，“你的年龄” 不会被影响。
250 + 1772 - y = a
2022 - y = a
and yes, the numbers were picked carefully, and the equation above makes simple sense: take 2022, minus the year you were born gets your age, which makes total sense
当然，这些数字是被小心筛选的，以上的方程式也非常明显说明：“拿2022，减去你的 出生年份，就能获得你的年龄”。
Can we use other numbers ? / 我们可以用其他数字吗 ?
let's try to come up with a formula to simulate the situation given
we will turn the given instructions into a set of "universal" instructions,
meaning not sticking with a specific input
我们可以尝试找出这一系列动作的公式：
| |
choose a number from 1 to 10, say this number is "t"，1-10 之间选择一个数字，设为"t" | t |
multiply it by "k", and add "d" to the result \\ 乘于 "k"，再加上 "d" | kt + d |
multiply the result by "s" \\ 将结果乘于 “s” | (kt + d)s |
add an off set, and lets call it "j" \\ 加上适当的错位，设为 "j" | (kt + d)s + j |
substract the year you were born from the result, let's call it "y" \\ 从结果减去出生年份，设为"y" | (kt + d)s + j - y |
and the result's hundreds is the number you have picked, the rest is your age, let's name it "a" \\ 三位数的 百位数是"t"，后面的两位数是我们的年龄，设为"a"。 | (kt + d)s + j - y = 100t + a |
by rearranging the fomular, we have the following
重新整理方程式，我们可以获得:
(kt + d)s + j - y = 100t + a
kst + ds + j - y = 100t + a
kst - 100t + ds + j - y = a
(ks - 100)t + (ds + j) - y = a
from the example given by GaoYuTian, we know that both 100t must be canceled out, or the coefficient of t must be 0, so we know that the first criterion is
从 高雨田大魔王 的例子，我们可以知道 100t 将会被抵消，也就是说 "t" 的系数 一定是0，所以我们可以知道第一个条件是：
ks - 100 = 0
ks = 100
we also noticed that 2022 just pop up "from no where",
and 2022 is the year when this post is posted, so we know that the second criterion is
当然我们也有注意到 2022 这个数字 “无缘无故” 的出现，
2022 是此贴发布的年份，所以我们可以推断出
ds + j - y = a
ds + j = y + a
ds + j = this year 今年年份
and that's all we need to know,
let's quickly come up with a new set of instructions to guess someone's age:
有了这些材料，我们就可以开始制作出一套新的“年龄计算配套”：
A quick Example / 例子
Step 1 \\ 步骤 1)
assign "k" and "s" a specific value, note they have to be a factor of 100, which can be
给 "k" 和 "s" 一个值，必须注意的是 "k" 和 "s" 必须是 100 的因数
if "k" is \\ 若 “k” 是 | then "s" is \\ 则 “s” 是 |
1 | 100 |
2 | 50 |
4 | 25 |
5 | 20 |
10 | 10 |
20 | 5 |
25 | 4 |
50 | 2 |
100 | 1 |
for the sake of demonstration, let's pick k = 5, s = 20
为了示范，我们可以选择让 k = 5, 让 s = 20
Step 2 \\ 步骤2)
assign "d" a specific value, this can be any natural number, let's pick 6 for example
给 “d” 一个值，可以是任何自然数，在这里我们选择 6
Step 3 \\ 步骤3)
find the value of "j", which we know ds + j = this year, so let's plug in the numbers and we will get
找出 "j" 的值，既然我们已将知道 ds + j = 今年年份，把 "d" 和 "s" 代入式中，我们可以获得
ds + j = this year 今年年份
(6)(20) + j = 2022
120 + j = 2022
j = 2022 - 120
j = 1902
Step 4 \\ 步骤4)
and now we will put everything into a set of instructions:
整理出一系列的步骤：
(1)
pick a number from 1 to 10
从 1-10 选一个数字
(2)
multiply it by 5 (=k), then add 6 (=d) to the result
乘于 5(=k) ,然后加上 6(=d)
(3)
take this result and multiply by 20 (=s)
用这个结果乘于 20(=s)
(4)
add 1902 (=j) to the result (post birthday),
or add 1901 to the result (pre birthday)
如果生日过了，加上 1902(=j)
如果生日还没过，加上 1901(=j)
(5)
take the result, minus the year you were born (=y)
减去 出生年份(=y)
(6)
now we have a result of 3 digits, the 1st one is the number you picked and the rest is your age
我们会获得一个三位数，百位数是你选择的数字，后面的两位数是你的年龄。and here we go, a new set of instructions just to "guess someone's age", have fun.
新的步骤出炉了，玩得开心点~
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