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The seesaw is filled with nine pairs of identical twins. All the kids weigh the same (e.g., they all weigh 100, but the actual numbers are irrelevant), except for one set of twins. They are still identical twins, so they weigh the same as each other, but not the same as the other 16 kids (e.g., these two children each weigh 101, but, again, the actual numbers are irrelevant). If (exactly) four kids on one side switch positions with four other kids on the other side to balance the seesaw, which is the odd pair?

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    $\begingroup$ So you're saying there is one pair of twins that weighs a different amount, and the rest weigh the same? $\endgroup$
    – Gabriel Burns
    Nov 7 '16 at 17:25
  • $\begingroup$ Yes 1 twin. 2 kids with same weight but unlike the rest causing the tilt $\endgroup$
    – TSLF
    Nov 7 '16 at 17:31
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    $\begingroup$ Just to fully clarify. Everyone always weighs the same as their twin, and everyone on the seesaw is a twin of someone else on the seesaw. In addition to weighing the same as their twin, everyone here actually has the same weight as everyone else, except for one pair that weigh differently (but still the same as each other)? Or is it just that every person with the same letter has the same weight as every other person with that letter (a less narrow constraint)? $\endgroup$
    – Rubio ♦
    Nov 7 '16 at 17:48
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    $\begingroup$ Have you taken into account the position on the seesaw beam? A kid that's 20kg heavier than the rest will have more effect on the outermost position of the seesaw than one that's at the innermost position. $\endgroup$
    – Ian MacDonald
    Nov 7 '16 at 18:20
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    $\begingroup$ Wish I could ^vote twice, after seeing the solution, once for each side of this clever puzzle $\endgroup$
    – humn
    Nov 7 '16 at 21:01
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The "odd" pair is

the O twins.

The way to balance the seesaw

is to change

ttl+eoevnn . wweove+lee
to

tWO+eLevEn = TweLve+ONe
(using capital letters to show the four and four that switched).  This cleverly "balances" the seesaw because it spells TWO+ELEVEN = TWELVE+ONE, i.e., 2+11=12+1.  After this switch, the O twins are both third from the end, so the seesaw balances even though they don't weigh the same as the others.  That is the only letter that is moved into a symmetric configuration.

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    $\begingroup$ I expected that somebody else would get it in the 10 minutes it took me to type the explanation. $\endgroup$
    – Peregrine Rook
    Nov 7 '16 at 17:54
  • $\begingroup$ @Peregine Rook- That is the Odd Twin. I expected it to be answered at least an hour and you are typing slow. Nice work. $\endgroup$
    – TSLF
    Nov 7 '16 at 18:21
  • $\begingroup$ What makes WWO+eLevnn ^ TTeLve+Oee unbalanced? $\endgroup$
    – Ian MacDonald
    Nov 7 '16 at 18:51
  • $\begingroup$ @IanMacDonald: It's lateral thinking wordplay.  WWO+eLevnn ^ TTeLve+Oee is gibberish; my solution balances the seesaw in a wordplay way. $\endgroup$
    – Peregrine Rook
    Nov 7 '16 at 18:54
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    $\begingroup$ @IanMacDonald finding two+eleven = twelve+one is balanced reveals the twins that are different. The worldplay shows us which twins are wrong. $\endgroup$
    – user64742
    Nov 8 '16 at 0:58

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