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If the biological cells are initially interchangeable, randomly allocate them to five groups of ten for the days. Within each day, independently choose a uniform distribution on a finite set over assignments having two occurrences of each dose level to the ten experimental units. One implementation is a random permutation of a list containing two labels of each level; the duplicate labels give every admissible assignment the same number of underlying permutations.

Randomize the processing order within each day as well, while pairing each preparation with its immediate measurement. Randomize dose within day, not merely the names of the days. This restricted randomization preserves the planned balance while protecting treatment contrasts against systematic order effects. Conceal the dose labels from the assessor where practical.

Start with six program sequences: $ABCABC$, $ACBACB$, $BACBAC$, $BCABCA$, $CABCAB$ and $CBACBA$. This gives two appearances of each program per row and per column. It also balances transitions: each ordered pair of distinct programs occurs five times across all adjacent sessions.

Apply restricted randomization by randomly assigning the six sequences to the six volunteers and independently permuting the three program labels. Using the supplied numbers, rank the first six from smallest to largest: the sequence indices are $(4,1,5,2,3,6)$. Assign these, in order, to volunteers 1 through 6. Rank the next three numbers attached to symbols $(A,B,C)$: their order is $(B,C,A)$. Assign actual program labels $(A,B,C)$ to these ordered symbols, so base $A\mapsto C$, base $B\mapsto A$, base $C\mapsto B$. The final ready-to-use randomized row-column design is:

Programs retain their real identities after this label permutation. The researcher should follow the table across chronological afternoons; arbitrary column permutations are deliberately excluded so that transition balance survives. Each program receives twelve sessions and occurs twice in every block. Under the additive block model, the analysis of variance has row, column, program and residual statistical degrees of freedom $5,5,2,23$, respectively, besides the grand mean. Transition balance is useful against differential carryover effects, but is not a proof that they are absent.

Restricted randomization samples assignments from a specified subset preserving features such as block balance, fixed group sizes or allowable treatment sequences. Inference must respect the chosen allocation scheme rather than treating all label permutations as admissible.