Card rules · 2026-10-29
Why Two Good Groups Can Still Share One Card Too Many
Seven cards cannot fill two four-card groups unless a card is counted twice. That sounds obvious when written as arithmetic. It is easier to miss when the same card completes both a…
Seven cards cannot fill two four-card groups unless a card is counted twice. That sounds obvious when written as arithmetic. It is easier to miss when the same card completes both a sequence and a set on screen.
Use a thirteen-card hand with no wild cards. Each card must belong to only one group. A sequence needs at least three consecutive cards of one suit; a set needs matching ranks in different suits. These requirements apply to the cards, not to the boxes drawn around them.
The card doing two jobs
Look at 6♦, 7♦, 8♦, 8♣ and 8♥. You can identify a diamond sequence, 6♦–7♦–8♦. You can also identify a set, 8♦–8♣–8♥. But you cannot submit both using these five physical cards: each combination needs the same 8♦.
The problem is not the rank order or the suits. Each group is valid when considered on its own. The conflict appears when they are claimed together.
Put the problem inside a full hand
Here are thirteen cards:
6♦ 7♦ 8♦ 8♣ 8♥ / 3♠ 4♠ 5♠ / J♥ Q♥ K♥ / 2♣ 2♦
The spade and heart sequences use six cards. Seven remain. If the diamond sequence uses 8♦, the other eights form only a pair. If the set uses 8♦, the diamonds are left as 6♦–7♦. The two twos also remain a pair. Drawing neat boxes around the cards does not supply the missing members.
One extra card can resolve one conflict
As a separate six-card exercise, add 8♠ to the original five-card collection. Now use 6♦–7♦–8♦ as the sequence and 8♣–8♥–8♠ as the set. There is no overlap: each physical card has one assignment.
This resolves that six-card exercise. It does not, by itself, complete the thirteen-card hand above. The twos and any required discard would still need consideration. Keeping those conclusions separate prevents a local improvement from being called a complete declaration.
How to inspect an arrangement
Write each physical card once, then assign it to one group. If two groups need the same card, one assignment must change. In a multi-deck exercise, two identical-looking cards may be separate physical copies; label them A and B rather than silently inventing a second copy.
A useful final question is: can the proposed groups be laid out using only the cards actually present, with no card repeated and none left over? If the answer is no, the arrangement is incomplete even when every individual box looks convincing.