No. In the documented Paplu variant, three-group hands are possible when their combinations satisfy the rules. The exercise below uses three natural runs, so four separate sorting boxes are not necessary.
A hypothetical five-plus-four-plus-four hand
This is a no-money paper-card exercise. Assume aces are wild; there are no aces in this inventory. Lay out the following thirteen separate cards:
- Hearts: two, three, four, five and six.
- Clubs: eight, nine, ten and jack.
- Diamonds: ten, jack, queen and king.
The first row contains five cards. The second and third contain four each. Five plus four plus four equals thirteen, and each row advances through consecutive ranks in one suit. No card is borrowed from another row, and no substitution is needed. These are three natural runs, not four groups compressed into three display boxes.
Why the total does not decide the grouping
Four plus three plus three plus three also equals thirteen. So does five plus five plus three. These are alternative ways to split a number, not proofs that any chosen cards fit those splits. To check a proposed arrangement, list the actual cards under each total. A blank box labelled four cannot certify the four cards inside it.
Keep the count, break the combination
For a counterexample, replace the king of diamonds with the seven of spades. There are still thirteen physical cards, and the row lengths remain five, four and four. However, the last row now reads ten, jack and queen of diamonds followed by seven of spades. Its fourth card does not continue either the rank track or the suit.
The failure is in that proposed row, not in the number three. Recounting thirteen cards will not repair it. Mark the exact card that breaks the row instead of adding another empty group.
Check the inventory before the layout
Count the cards, draw boundaries around the proposed rows, and check rank, suit and physical identity within each row. A particular application's sorting slots are not evidence of a universal grouping rule. This example concerns the specified Paplu exercise only, not every product called rummy.