Use logical elimination

Detailed Explanation: Use logical elimination

When a problem gives several clues, start by listing every possible case. Then use each clue to cross out cases that cannot work. The answer is the case—or cases—that remain after all clues are used.

Example

A locker number is one of the numbers from $1$ to $12$.

• It is even.
• It is greater than $5$.
• It is less than $10$.
• It is not a multiple of $3$.

What is the locker number?

Step 1: List all possibilities

This list is important because it shows that we are considering every possible locker number.

Step 2: Use the first clue

The number is even, so cross out the odd numbers:

Step 3: Use the second clue

The number is greater than $5$, so remove $2$ and $4$:

Step 4: Use the third clue

The number is less than $10$, so remove $10$ and $12$:

Step 5: Use the last clue

A multiple of $3$ is a number in the $3$ times table. Of the remaining numbers, $6$ is a multiple of $3$, so remove it:

Step 6: Check the answer

The number $8$ is:

• even,
• greater than $5$,
• less than $10$, and
• not a multiple of $3$.

Only $8$ remains, so the locker number must be $\boxed{8}$. This is not a guess because every possible number was considered and every other number was ruled out by a clue.