Logic
Arithmetic Puzzles
What series of signs will make the following equation true: \[ 2 \, \square \, 2 \, \square \, 2 \, \square \, 2 = -6? \]
Which of the following series of signs will make the following equation true: \[ 2 \, \square \, 2 \, \square \, 2 \, \square \, 2 = 4? \]
What series of signs will NOT make the following equation true: \[ 8 \, \square \, 8 \, \square \, 8 \, \square \, 8 = 0? \]
How many different 3-tuples \((\square,\triangle,\star)\) of operators make the following equation true: \[6 \, \square \, (3 \, \triangle \, 2)=1 \, \star \, 1?\]
Details and Assumptions
- \(\square,\triangle,\star\) can be one of the four arithmetic operators: \(+,-,\times,\div.\)
- One kind of operator can be used more than once.
What series of signs will NOT make the following equation true: \[ 4 \, \square \, 4 \, \square \, 4 \, \square \, 4 = 16? \]