# Interview Prep: Logic and Math Problems You Should Know 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.