Imperial Examination Question 帝国考试题

Thanks to Cynthia (who wants to remain anonymous) for supplying the question for us to activate our minds.

感谢 Cynthia（希望保持匿名）为我们提供问题以激活我们的思想。

Gǎnxiè Cynthia(xīwàng bǎochí nìmíng) wèi wǒmen tígōng wèntí yǐ jīhuó wǒmen de sīxiǎng.

The question below was handed to the examination candidates circa 1900. The candidates were in their self-contained boxes for three days, two nights.

The question was to be answered within an hour. Now it is our turn to see if we can answer this question within the hour.

下面的问题是在 1900 年左右交给考生的。考生在自备的箱子里待了三天两夜。
Xiàmiàn de wèntí shì zài 1900 nián zuǒyòu jiāo gěi kǎoshēng de. Kǎoshēng zài zì bèi de xiāngzi lǐ dàile sān tiān liǎng yè.
这个问题应该在一个小时内得到回答。现在轮到我们看看我们能否在一小时内回答这个问题。
Zhège wèntí yīnggāi zài yīgè xiǎoshí nèi dédào huídá. Xiànzài lún dào wǒmen kàn kàn wǒmen néng fǒu zài yī xiǎoshí nèi huídá zhège wèntí.

Add mathematical symbols in-between the three numbers 3 7 5 such that the answer to the question results in an answer of 1. No, that is not all. Think again to get a result of 2, then 3, then 4 right through to a result of 21.

在三个数字 3 7 5 之间添加数学符号，使问题的答案为 1。不，这还不是全部。再想一想，结果是 2，然后是 3，然后是 4，直到结果是 21。
Zài sān gè shùzì 3 7 5 zhī jiān tiānjiā shùxué fúhào, shǐ wèntí de dá'àn wèi 1. Bù, zhè hái bùshì quánbù. Zài xiǎng yī xiǎng, jiéguǒ shì 2, ránhòu shì 3, ránhòu shì 4, zhídào jiéguǒ shì 21.

That is to say: 3 7 5 = 1

Then: 3 7 5 = 2

Then: 3 7 5 = 3

On the Examination Board was Emperor Guangxu.

考官上有光绪皇帝。Kǎoguān shàng yǒu guāngxù Huángdì.

Another Examiner of that period - young and talented Minister Liang Wenxiu.

那个时期的另一位考官——年轻有为的梁文秀部长。
Nàgè shíqí de lìng yī wèi kǎoguān——niánqīng yǒu wéi de liáng wénxiù bùzhǎng.

Let us pause here for us to have a crack at the question - 21 lines in total.  让我们在这里暂停一下，让我们破解这个问题——总共 21 行。
Ràng wǒmen zài zhèlǐ zàntíng yīxià, ràng wǒmen pòjiě zhège wèntí——zǒnggòng 21 xíng.

“Time’s Up,” yelled the Chief Invigilator and echoed by the rest of the invigilating team. “Stop writing, Time’s up. Place the answer paper to your right, stand up and leave. Come back by 2:00 pm this afternoon for your next examination on writing suitable ‘Couplets’.”

“时间到了。”总监考员喊道，其他监考队员也纷纷附和。 “别写了，时间到了。把答卷放在你的右边，起身离开。今天下午2:00回来参加你下一次写合适的'对联'的考试。”
“Shíjiān dàole.” Zǒngjiānkǎo yuán hǎn dào, qítā jiān kǎo duìyuán yě fēnfēn fùhè. “Bié xiěle, shíjiān dàole. Bǎ dájuàn fàng zài nǐ de yòubiān, qǐshēn líkāi. Jīntiān xiàwǔ 2:00 Huílái cānjiā nǐ xià yīcì xiě héshì de'duìlián'de kǎoshì.”

Now let us compare our answers with the actual answers below:

3⁰ x 7⁰ x 5⁰ = 1

3 - (7⁰ x 5⁰) = 2

3 x (7⁰ x 5⁰) = 3

3 + (7⁰ x 5⁰) = 4

(3⁰ x 7⁰) x 5 = 5

(3⁰ x 7⁰) + 5 = 6

3⁰ x 7 x 5⁰ = 7

3 x 7⁰ + 5 = 8

3² x 7⁰ x 5⁰ = 9.           or.          3 + 7 - 5⁰ = 9

(3 + 7) x 5⁰ = 10 

3 + 7 + 5⁰ = 11.           or.          3² + 7 - 5 = 11     

(3⁰ x 7) + 5 = 12

3⁰ + 7 + 5 = 13

3² x 7⁰ + 5 = 14

3 + 7 + 5 = 15

3 x 7 - 5 = 16

3² + 7 + 5⁰ = 17.         or.       -3² + 7⁰ + 5² = 17

3² x (7 - 5) = 18  

3⁰ - 7 + 5² = 19.         or.      3³ - 7 - 5⁰ = 19

(-3 + 7) x 5 = 20.       or.      (3 + 7⁰) x 5 = 20

3² + 7 + 5 = 21.