Question 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 I cannot enter the calculation $2\times14$ 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?