What is a distributive property​

In mathematics, the distributive property of binary operations generalizes the distributive law from elementary algebra, which asserts that one has always {\displaystyle x\cdot =x\cdot y+x\cdot z.} For example, one has 2 ⋅ = +. One says that multiplication distributes over addition. 

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.