Daily Challenge 

Seven zebras, thirteen hyenas, and two lions find themselves alone in MathsSavannah. Hyenas can eat zebras. Lions can eat both hyenas and zebras. MathsSavannah is fantastic:​ If a hyena eats a zebra, it transforms into a lion;​ If a lion eats a hyena, it transforms into a zebra;​ If a lion eats a zebra, it transforms into a hyena.​ After some time, no animal can eat another; an equilibrium is reached. The number of remaining animals is as large as possible. What is this number?

Given 10 lines on a plane, what are the possible numbers of intersection points?

Let 𝑚 < 𝑛 be positive integers. Start with 𝑛 piles, each of 𝑚 objects. Repeatedly carry out

the following operation: choose two piles and remove 𝑛 objects in total from the two piles.

For which (𝑚, 𝑛) is it possible to empty all the piles?

七只斑马、十三只鬣狗和两只狮子独自来到数学草原。 鬣狗可以吃斑马。 狮子可以吃鬣狗和斑马。 数学草原很奇妙：​

• 如果一只鬣狗吃了一只斑马，它会变成一只狮子；​

• 如果一只狮子吃了一只鬣狗，它会变成一只斑马；​

• 如果一只狮子吃了一只斑马，它会变成一只鬣狗。​

一段时间后，没有动物可以再吃其他动物，达到了平衡状态。 剩下的动物数量尽可能多。 这个数字是多少？

给定平面上的10条直线，可能的交点数量有哪些?

令 𝑚 < 𝑛 为正整数。开始时有 𝑛 堆，每堆 𝑚 个物体。反复执行以下操作：选择两堆并从这两堆中总共移除 𝑛 个物体。对于哪些 (𝑚, 𝑛) 组合，可以将所有堆清空