Logic

Arithmetic Puzzles

Fill in the Blanks Warmup

         

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

×=11? \square \, \times \, \square = 11 ?

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

8÷8=3 8 \square \div \bigcirc 8 = 3

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


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

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

2×4=8? \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:

1×=9? \Large 1 \square \times \square = \square 9 ?

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