Is the key hidden among the dining-cart foods?

No. The book-shaped food menu is a decoy and never produces the key.

Where is the real key in Level 62?

It sits along the bottom of the Level Selection screen beside the Boxy mascot.

Tap it in Level Selection and reopen Level 62; it then appears and drops beside the dining cart.

Brain Riddle: Tricky Box level guide

medium 5 colors

Leave the room through the pause menu, take the gold key from Level Selection, reopen Level 62, and carry the spawned key to the chained right door.

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Ignore the dining cart's gold book control because it only cycles meals and drinks in thought bubbles.
Tap the pause icon in the top bar, then choose Menu on the white pause card.
On Level Selection, tap the small gold key lying along the bottom edge beside the Boxy mascot.
Select the Level 62 badge to enter the room again and wait for the gold key to drop beside the dining cart.
Move Boxy right through the chair-and-cart area until he touches and collects the key.
Continue to the chained pink door; let the key remove its lock, enter the opened portal, and confirm the Congratulations overlay.

Colors in this level:

Pink, Gold, White, Brown, Purple

Cycling every dish in the food menu and expecting one of the thought bubbles to become a key.
Opening the pause card but choosing Resume instead of Menu.
Returning to the chained door before re-entering Level 62 and collecting the spawned gold key.

Stop if food pictures are appearing above Boxy; that is the wrong menu.
Look beside the Boxy mascot at the bottom of Level Selection for the small gold key.
Reopen Level 62 before trying to collect the key inside the room.

Board notes 5 details

Layout: Boxy starts by an open left door in a dining room with a white chair, a wheeled food cart, a book-shaped food-menu control, and a chained pink door on the right.
Goal: Retrieve the persistent gold key from Level Selection, collect it beside the cart after re-entering Level 62, and unlock the right exit.
Opening: The cart's gold book button only cycles food thought bubbles; use the top pause button and choose Menu on the pause card instead.
Danger Zone: The word menu points at a decoy list of meals, while the useful gold key is outside the room along the bottom of the Level Selection screen.
Mechanics: A key collected in the outer level menu persists across a reload and materializes inside Level 62 for Boxy to pick up.

Is the key hidden among the dining-cart foods?
No. The book-shaped food menu is a decoy and never produces the key.
Where is the real key in Level 62?
It sits along the bottom of the Level Selection screen beside the Boxy mascot.
How does the key get back into the room?
Tap it in Level Selection and reopen Level 62; it then appears and drops beside the dining cart.