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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.

Level 3

         

\[ \large \square \ + \ \square \ - \ \square \ \times \ \square \ \div \ \square \]

You are given that the numbers \(1,2,3,4\) and \(5\) are to be filled in the square boxes as shown above (without repetition).

By strictly applying the operations from left to right (without adhering to order of operations), find the minimum possible value of the resultant number. Give your answer to 3 decimal places.

\[ \large \square + \square\square+\square\square\square+\square\square\square\square \]

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 \( 1 \times \square \).

\[ \large \square + \square\square+\square\square\square+\square\square\square\square \]

You are given that the numbers \(0,1,2,\ldots,9\) are to be filled in the square boxes as shown above (without repetition) such that it represent a sum of a 1-digit, 2-digit, 3-digit, and 4-digit number.

Find total number of possible arrangements of these nine numbers such that the sum of these four numbers is maximized.

Details and Assumptions:

  • For the purposes of this question, 0 is considered a 1-digit number.
  • 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 \( 1 \times \square \).

Using the digits 1 through 9 without repetition, fill out the number grid above. What is the product of the numbers in the 4 corners?

Note: The order in which this grid calculates is left-to-right/top-to-bottom unlike the usual order of operations. E.g., \(1+2\times 3 = (1+2)\times3=9.\)

\[ \large 1 \, \square \, 2 \, \square \, 3 \, \square \, 4 \, \square \, 5 \, \square \, 6 \, \square \, 7 \, \square \, 8 = 9 \]

There are \( 2^7 =128 \) ways in which we can fill the squares with \( +, -\).

How many ways would make the equation true?

Note: You are not allowed to use parenthesis.

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