Can You Solve the Math Olympiad Question in 2 Minutes?

Learn how to solve a Math Olympiad question using basic math concepts and reasoning

Math Olympiad Question: 2^a + 2^b + 2^c = 148, a, b, c = ?. Can you solve in 2 minutes? Use basic math concepts and reasoning.

Recommended time to solve: 2 minutes.

First, try to solve all by yourself. With the math reasoning and basic concepts, the problem shouldn't be hard to solve.

Solution: Math Olympiad Question Solution on Exponents of 2

Problem puzzle: 2^a + 2^b +2^c = 148, a, b, c = ?

Unis digit analysis of powers of 2

Unit digits: for 2¹ => 2, 2² => 4, 2³ => 8, 2⁴ => 6, 2⁵ => 2, 2⁶ => 4, 2⁷ => 8, 2⁸ => 6 again the unit digits 2, 4, 8, 6 cycle for all powers of 2.

How to choose 3 exponents of 2 for a sum of 148 with unit digit 8?

Possible combinations of unit digits for exponents of 2 for the sum to have unit digit 8:

2 + 2 + 4 => 8

4 + 6 + 8 => 8

These are the only two possible combinations for powers of 2 to produce sum with unit digit 8.

Logical reasoning

• To reach a sum close to target one of the powers must be large. Unit digit 8 satisfies the criterion. It must be one of the values of a, b or c.

Only possibility: The Solution

2² + 2⁴ + 2⁷ = 4 + 16 + 128 = 148.

a = 2, b = 4, c = 9, with all three values interchangeable.

A real quick solution. Should be well within the time limit.

More puzzles for you

Easy to hard categorized brain teasers with systematic solutions from SureSolv.com:

Challenging brain teasers with solutions: Long list.

Good luck to your problem-solving!