Ever stumbled on a reasoning test and thought, “I used to know this”? You’re not alone. We see algebra, logic, and math throughout school and college — but if you’re not using them daily, those skills can fade fast.

I recently have brushed off some common problems you may encounter in interviews that aim to assess your sharpness and problem-solving skills. Here’s a curated list of common problems so you can be ready when it happens to you:

1- Permutation Problem (Arranging all elements)

How many different ways can the letters in the word "ROSE" be arranged?

There are 4 distinct letters in "ROSE", and we want to know how many different ways we can arrange all of them (where order matters).

Since we are including all the elements and the order matters (OSER is not the same as OSRE), we use the permutation formula:

$$P(n)=n!$$

$$P(4)=4!=4×3×2×1=24$$

Answer: There are 24 different ways to arrange the letters in "ROSE".

2- Permutation Problem (Arranging Some, Not All, Elements)

A teacher needs to assign 1st, 2nd, and 3rd place prizes to 3 students from a group of 8 finalists. How many different ways can the top 3 prizes be awarded?

Since the order matters (1st ≠ 2nd ≠ 3rd), we use the partial permutation formula:

$$P(n, r) = \frac{n!}{(n - r)!}$$

$$P(8, 3) = \frac{8!}{(8 - 3)!}$$

Simplify:

$$P(8, 3) = \frac{8 \times 7 \times 6 \times 5!}{5!}$$

Cancel (5!):

$$P(8, 3) = 8 \times 7 \times 6 = \boxed{336}$$

Answer: There are 336 different ways to assign 1st, 2nd, and 3rd place to 3 students from a group of 8.

3- Combination Problem

In a room of 8 people, if each person shakes hands with every other person once, how many handshakes occur?

Each handshake involves a pair of people, and the order doesn’t matter — so we use combinations, not permutations. We want to choose 2 people out of 8, we need the combination formula:

$$C(n, r) = \binom{n}{r} = \frac{n!}{r!(n - r)!}$$

$$\binom{8}{2} = \frac{8!}{2!(8 - 2)!}$$

Simplify:

$$\binom{8}{2} = \frac{8 \times 7 \times 6!}{2 \times 1 \times 6!}$$

Cancel (6!) from top and bottom:

$$\binom{8}{2} = \frac{8 \times 7}{2 \times 1} = \frac{56}{2} = \boxed{28}$$

Answer: There are 28 unique handshakes.

4- Average Problem (Solving a First-Grade Equation):

In April, there were 120 new users, and in May, 135. If the average number of users for the second quarter was 180 per month, how many users were made in June?

To solve this problem we use the Average or mean formula to have an equation and then we solve for x:

$$\text{Average} = \frac{\text{April} + \text{May} + \text{June}}{3}$$

$$180 = \frac{120 + 135 + x}{3}$$

$$180 \cdot 3 = 255 + x$$

$$540 = 255 + x$$

$$x = 540 - 255 = \boxed{285}$$

Answer: 285 new users in June.

5- Number Sequence — What Comes Next?

a) Given the sequence: 5, 8, 13, 20, 29

What is the next number?

These types of problems are all about pattern recognition. In this case we calculate the differences between consecutive numbers:

8 − 5 = 3
13 − 8 = 5
20 − 13 = 7
29 − 20 = 9

We observe that the differences increase by 2 each time:

3, 5, 7, 9 → The next one is 11

We add the next difference to the last number:

29 + 11 = 40

Answer: 40 is the next number on the sequence

b) Given the Sequence: 64, 32, 16, 8. What is the next, number?

Each term is divided by 2:
64 → 32 → 16 → 8 → 4

✅ Answer: 4

🎯 Final Thoughts

These types of reasoning problems — whether it's permutations, averages, sequences, percentages, financial reasoning, or word problems that translate into simple equations or systems of equations — might feel like school math at first, but they’re sometimes used in interviews to assess a candidate’s sharpness and problem-solving skills.

While not every company includes them, they do show up — especially in remote or international roles where quick thinking and adaptability are valued.

So if you’re interviewing beyond your borders, brushing up on these skills is still an advantage — particularly because many candidates overlook them. A bit of preparation may help you stand out when it counts.

Interview Prep: Logic and Math Problems You Should Know