Prove: The square of the sum of two consecutive integers is odd.
(n + (n + 1))2= ([ ? ]n + 1)2
= [ ]n2 + [ ]n + []
= 2([ ]n2 + [ ]n) + 1
= odd

(n + (n + 1))²

= (2n + 1)²

= 4n² + 4n + 1

= 2(2n² + 2n) + 1

= odd

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.

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol