# One does not belong. (But they are all wrong, aren't they?)

One of these six equations below does not belong to the group. Which one? and why? Text

10+14=23

10+15=24

10+16=25

10+17=26

10+18=27

10+19=28

I think the secret to this puzzle lies away from mathematics. After all, each of the equations makes no mathematical sense in base-10 (i.e. 'they are all wrong', as the title attests). Instead, we should:

count up the number of letters in each of the numbers written out in English. Once we do that, five of the 'equations' are balanced, with the same number of letters on either side of the equals sign, and just one is not:

 TEN + FOURTEEN = TWENTY THREE 
 TEN + FIFTEEN = TWENTY FOUR 
 TEN + SIXTEEN = TWENTY FIVE 
 TEN + SEVENTEEN = TWENTY SIX 
 TEN + EIGHTEEN = TWENTY SEVEN 
 TEN + NINETEEN = TWENTY EIGHT 

This way, the fourth 'equation' is the odd-one-out.

• "I think the secret to this puzzle lies away from mathematics." Not much of a "secret", really, considering three and a half out of four answers don't even mention maths... Apr 19, 2021 at 8:54

The odd one out is

10 + 19 = 28

Because

All of the equations are correct if you interpret the second addend in base 9, but you can't have a 9 digit in base 9.

• That is like saying "the last one is the odd one out because it's the only one at the end of the list"... kind of just making a rule up to fit a random answer. Apr 19, 2021 at 12:00
• No, the poster would be correct even if the list were re-ordered. it isn't his fault the OP included no other 9s. Apr 19, 2021 at 21:03

Maybe

10+15=24.

Because it's the only one that's actually right, in a sense.

(2 strokes to write 10 and 4 strokes to write 15 = 2&4, or 24).

• Do you write 5 in 3 strokes? Isn't it 1 stroke like every other letter, or 2 if you don't like going backwards with your first stroke? Apr 19, 2021 at 12:13
• I just counted distinct lines and curves, but it is certainly a long shot. I imagine this question has lots of solutions.
– Amoz
Apr 19, 2021 at 12:46

Is it

the second one? 15 being the only teen that does (phonetically) change its non-teen bit, "fifteen", not "fiveteen" ("thirteen is not in the list and "eighteen" sounds the same as "eightteen" would).

• Not really @loopy walt. Gur gvgyr vf n pyhr
– DrD
Apr 18, 2021 at 23:19