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Arithmetic Puzzles

Arithmetic puzzles are Mad Libs for math: fill in the blanks with numbers or operations to make the equation true.

Fill in the Blanks

         

Can we place a single digit in each \( \square \), such that the following equation is true:

\[ \square \, \times \, \square = 11 ? \]

What (possibly different) single digit should we place in \( \square \) and \( \bigcirc\) to make the following equation true:

\[ 8 \square \div \bigcirc 8 = 3 \]

Give your answer as \( ( \square, \bigcirc ) \).


This is an arithmetic puzzle, where \( 8 \square \) would represent the 2-digit number 89 if \( \square = 9 \). It does not represent the algebraic expression \( 8 \times \square \). The same logic applies for the 2-digit integer \( \bigcirc 8\).

Does there exist (possibly different) digits which we can replace the \( \square \) with, to make the following expression true:

\[ \square 2 \times 4 = \square 8 ? \]

If in each of the squares, we must fill in a distinct digit, what is the minimum possible positive value of the difference?

\[ \begin{array} { l l l }
& \square & \square \\ - & \square & \square \\
\hline \end{array} \]

What identical digit can we place in \( \square \), to make the following statement true:

\[ \Large 1 \square \times \square = \square 9 ?\]

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