What do you mean by "No.1", "No.2" and "flower exploration"?

The number one scholar means: palace examination won the first place in the imperial examination.

The second place refers to palace examination's second place in the imperial examination.

Flower exploration refers to: palace examination's third place in the imperial examination.

Extended data:

Champion, champion and champion refer to the top three in the imperial examination.

Palace examination is the highest subject in the imperial examination. The emperor took the exam and asked questions. The first one is for Jinshi and, the second one is for Jinshi origin, and the third one is for Jinshi origin. The first one admitted three students, the first one is commonly known as the number one scholar, the second one is commonly known as the second one, and the third one is commonly known as Tan Hua, which is collectively called Sandingjia.

References:

Imperial Examination System-Baidu Encyclopedia