The Cookie Tin Mix-Up

Can you relabel the tins like Penelope did?
At the Maple Creek holiday market, the vendor’s daughter mischievously swapped the labels on three tins of cookies. Now, each tin is incorrectly labeled. Penelope is allowed to inspect one cookie at a time – without looking inside the tins.

What’s the fewest number of cookies she needs to inspect to figure out the correct labels?

Make your selections below to see if you’ve solved it like Penelope.

All three labels are wrong. That’s your biggest clue.

Try drawing the three tins and listing what each could contain, knowing the labels are incorrect.

If you pull a cookie from the tin labeled “Mixed,” it can’t be mixed—so it must be all one type. That tells you what’s really inside.

Start with the tin labeled “Mixed.” Whatever cookie you pull out is the only kind in that tin. From there, work backwards using process of elimination to fix the other two labels.

You only need to inspect one cookie from the tin labeled “Mixed.”

Since all labels are wrong, the “Mixed” tin cannot actually contain mixed cookies.
So, whatever type of cookie you pull out (e.g., Sugar) must be the only type in that tin.

Now relabel:

  • The tin labeled “Mixed” actually contains Sugar (or whichever you drew).

  • The tin labeled “Gingerbread” cannot be Gingerbread, and it cannot be Sugar (since that’s already taken), so it must be Mixed.

  • The tin labeled “Sugar” must be the remaining type: Gingerbread.

By checking just one cookie, you can correctly relabel all three tins.