×

Arithmetic Puzzles

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

Level 2

$\large 1 \, \square \, 2 \, \square \, 3 \, \square \, 4 = 10$

There are $$4^3 = 64$$ ways in which we can fill the squares with $$+ , - , \times , \div$$.

How many ways would make the equation true?

Note:
You are not allowed to use parenthesis.
Obey the order of operations.

$\left(\color{green}{\square}5\right)^2 = \color{blue}{\square}25$

Each square above represents a positive integer. Let $$m$$ and $$n$$ denote the values that fill in the green and blue squares, respectively, satisfying the equation. Then what is the relationship between $$m$$ and $$n?$$

Details and Assumptions:

• This is an arithmetic puzzle, where $$1 \square$$ would represent the 2-digit number 19 if $$\square = 9$$. It does not represent the algebraic expression $$1 \times \square$$.

In the figure above, each letter represents a distinct single digit among $$0, 1, 2, \ldots, 9.$$ They are positioned in such a way that $\large A\times B\times C=B\times G\times E=D\times E\times F.$

What digit does the letter $$G$$ represent?

$\large \square + \square\square+\square\square\square+\square\square\square\square$

Place each of the digits 0 through 9, without repetition, in the boxes above. Then what is the maximum possible sum?

Details and Assumptions:

• This is an arithmetic puzzle, where $$1 \square$$ would represent the 2-digit number 19 if $$\square = 9$$. It does not represent the algebraic expression $$1 \times \square$$.

$\LARGE \square^{\square^{\square^{\square}}}$

You are given that the numbers $$1,2,3,4$$ are to be filled in the square boxes as shown above (without repetition). Of all $$4!=24$$ possible arrangements, find the total possible arrangements of these numbers such that the resultant number is a minimum.

Details and Assumptions

As an explicit example, a possible value of the resultant number is $$\large 2^{3^{1^4}} = 8$$.

×