Title: From a certain day on, the white hen 1 laid three eggs, the black hen laid three eggs 1 egg, and two hens laid 100 egg. How many days will it take?

After thinking about it, I found that the topic "Starting from a certain day" did not specify whether the chicken laid eggs or rested, so there was more than one kind of drawing. There are 16 drawing methods (with "○" for chicken laying eggs and "□" for chicken not laying eggs).

(1) White hen: ○□, ○□, ○□. ...

Black hen: ○□□□□□□, ○□□□□□, ○□□□□ …

(2) White hens: 0000, 0000, 0000. ...

Black hen: ○□□□□□□, ○□□□□□, ○□□□□ …

(3) White hen: ○○○○○○○○○○○○○○○○ ...

Black hen: ○□□□□□□, ○□□□□□, ○□□□□ …

(4) White hen: □??χ

Black hen: ○□□□□□□, ○□□□□□, ○□□□□ …

The above is just the change of white hen's egg rest. Black hens always lay 1 egg from this day and rest for 3 days. If the black hen has also changed, there are three situations for each white hen, namely □□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□

By comparison, I found that there are actually two answers to the number of days required for white hens and black hens to lay 100 eggs. In all the lottery methods of 16, when the white hen and the black hen are born to the 96th egg (that is, it takes 96 days), four eggs are regenerated. If the white hen and the black hen rest at the same time on the last day, it actually takes only 99 days (for example, the lottery method 1, 5, 6); If only one white hen and one black hen have a rest or neither of them has a rest on the last day, it actually needs 100 days (for example, 2, 3, 4, 7~ 16). So there should be two answers to this question, that is, it takes 99 days for a white hen and a black hen to lay 100 eggs or 100 days.

Instructor: Shi

five

White hen: ○○□

Black hen: □□□□□□□□ 8

White hen: ○ □

Black hen: □□□□□□□11

White hen: ○○□

Black hen: □□□□□□14

White hen: □

Black hen: □○□□

six

White hen: ○○□

Black hen: 9

White hen: ○ □

Black hen: □□□□□□12

White hen: ○○□

Black hen: □□□□□□15

White hen: □○○○ Black hen: □□○□

seven

White hen: ○○□

Black hen: □□□□□○10

White hen: ○ □

Black hen: □□□□□○13

White hen: ○○□

Black hen: □□□□□○16

White hen: □○○○ Black hen: □□□