Logic
# Arithmetic Puzzles

\[ \large \left( \square \ + \ \square \ - \ \square \ \right) \times \ \square \ \div \ \square \]

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).

Find the **minimum** possible value of the resultant number. Give your answer to 3 decimal places.

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

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 ten 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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