$l (i, 47 - j) = l (i, 47 - \hat{j}) = 1 + \frac{q_{47 - j} \times q_{47 - \hat{j}}}{q_{j} \times q_{\hat{j}}} (\frac{r_{i}}{210} + l (i, j) - 1) - \frac{r_{i}}{210}$ .

(ii) For $l (i, j) = l (i, \hat{j})$ , for $1 \leq j \leq 23$ but not for $\hat{j}$ , then $24 \leq \hat{j} \leq 46$ and $q_{\hat{j}} = \frac{r_{i} + 210 [l (i, j) - 1]}{q_{j}}$ .