Making 6,843 with playing cards

In this video, Scott Wu from Cognition builds 6,843 with playing cards in seconds. The shortcut is to work backward from the target.

The eight-card proof

The values are 12, 10, 10, 10, 8, 11, 7, 3. Jacks count as 11 and queens as 12; the pictured suits are illustrative.

Every card appears once:

Work backward

First, $6843=3\cdot2281$. Then $2281=11\cdot208-7$. This reserves the 3, 11, and 7. The rest follow from $208=200+8$ and $200=(12-10)\cdot10\cdot10$. Each step leaves a smaller target made from the cards still available.

Why the solver works

For four cards, the tool records every integer reachable from each subset of cards. It combines two disjoint subsets with $+$, $-$, $\times$, or exact division, keeping one expression for each result.

This covers every allowed expression: its last operation must join two smaller expressions on disjoint sets of cards. Repeating that argument reaches the individual cards. So a result uses each card once, and a missing result cannot be made under these rules. The tool requires integer intermediate values; it does not use powers or join digits.