## 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 2^{1} => 2, 2^{2} => 4, 2^{3} => 8, 2^{4} => 6, 2^{5} => 2, 2^{6} => 4, 2^{7} => 8, 2^{8} => 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

2^{2} + 2^{4} + 2^{7} = 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.

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Good luck to your problem-solving!