Multiplication is the most powerful operator

Logic Level 2

$\large 1 \; \square \; 2 \; \square \; 3 \; \square \; 4 \; \square \; 5 \; \square \; 6$

Fill in the boxes above with any of the four mathematical operators ( $+, -, \times , \div$ ). What is the maximum possible resultant number?

Note : Order of operations (BODMAS) applied.

719 721 722 720

2 solutions

A Former Brilliant Member
Jul 1, 2016

The maximum value is $1+2 \times 3 \times 4 \times 5 \times 6=\boxed{721}$ .

The (slightly) hard part is to prove that it is indeed the maximum value.

Pi Han Goh - 4 years, 11 months ago

Start from the left. To maximize $1 \square 2$ , we use the operation addition. From there to maximize the value, we use multiplication.

A Former Brilliant Member - 4 years, 11 months ago

Wonderful! Wonderful

Pi Han Goh - 4 years, 11 months ago

Munem Shahriar
Nov 27, 2017

We will not use $\div$ and $-$ . Because it will decrease the result.

So we have two possibilities:

$1 \times 2 \times 3 \times 4 \times 5 \times 6 = 720$

$1 + 2 \times 3 \times 4 \times 5 \times 6 = 721$

Since $721 > 720$ , $\boxed{721}$ is the largest possible result.

The (slightly) hard part is to prove that it is indeed the maximum value.

Pi Han Goh - 3 years, 6 months ago