30. The '4' button on my calculator is spoilt, so I cannot enter numbers which contain the digit 4. Moreover, my calculator does not display the digit 4 if 4 is part of an answer either. Thus $\mathrm{I}$ cannot enter the calculation $2 \times 14$ and do not attempt to do so. Also, the result of multiplying 3 by 18 is displayed as 5 instead of 54 and the result of multiplying 7 by 7 is displayed as 9 instead of 49 . If I multiply a positive one-digit number by a positive two-digit number on my calculator and it displays 26 , how many possibilities could I have multiplied?
30. Ans: 6 .
Since the product is at most a three-digit number, the possible answers I should get is $26,426,246$ or 264 . Since
$$
\begin{aligned}
26 & =1 \times \mathbf{2 6}=\mathbf{2} \times \mathbf{1 3} \\
426 & =1 \times 426=2 \times 213=3 \times 142=\mathbf{6} \times \mathbf{7 1} \\
246 & =1 \times 246=2 \times 123=\mathbf{3} \times \mathbf{8 2}=6 \times 41 \\
264 & =1 \times 264=2 \times 132=\mathbf{3} \times \mathbf{8 8}=4 \times 66 \\
& =6 \times 44=8 \times \mathbf{3 3}=11 \times 24=12 \times 22,
\end{aligned}
$$
there are 6 possibilities.