Teeter -Totter

[TimeSpaceLightForce]

1) How can the you balance the see-saw by exchanging any 2 kids position 4 times?
2) Which twin weighs different from others?

[plainglazed]

from left side to right side; left to right:

switch the second T with the first W

switch the first L with the first O

switch the first O with the first L

switch the first N with the third E

[bonanova]

Swap the red kids:

T T L + E O E V N N ^ W W E O V E + L E E
E T L + E O E V N N ^ W W E O V E + L T E
E T L + E O E V W N ^ N W E O V E + L T E
E T L + E V E O W N ^ N W E O V E + L T E
E T L + E V E O W N ^ N W O E V E + L T E <= final balanced position

Which twins weight different?

If the last three swaps are done first, we have this position

T T L + E V E O W N ^ N W O E V E + L E E,

which is symmetrical except for the outer T T vs E E.

If this still unbalanced to the left, and I don't see

how we could conclude that, then we could conclude

that TT are heavier than EE.

But since OP asks only to identify difference from all

others, not one heavier or lighter than another, then

a different configuration likely holds the answer.

[TimeSpaceLightForce]

That is it ! Bonanova's arrangement got it balanced. That is the same symmetric solution I got.

But unlike odd weight balance scale problem, this one has a predetermined odd weight and

should have a 'leading clue' i.e. not symmetric - the anagramatist equation . Plainglazed solution shows:

T W O + E L E V E N = T W E L V E + O N E all E's are same weights , so only the O's are odds then.

Thanks for solving..more power !