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 ^@3 \times 24^@ 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 ^@6^@ by ^@8^@ is displayed as ^@8^@ instead of ^@48^@. 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?
Answer:
^@6^@
- The possible results when a positive ^@1-^@digit number is multiplied by a positive ^@2-^@digit number that will display ^@26^@ is ^@26, 426, 246, \text{ and } 264^@.
- ^@\begin{align} & 26 = 2 \times 13, 1 \times 26 \\ & 426 = 6 \times 71\\ & 246 = 3 \times 82\\ & 264 = 3 \times 88, 8 \times 33 \end{align}^@
- Hence, there are ^@6^@ such possibilities.
