Question

What is the largest number you can get by composing an arithmetic expression from the digits 1, 2, 3, 4, 5, and 6 and the signs of four arithmetic operations, if you can use each digit exactly once?

a) 720
b) 721
c) 722
d) 723

Answer 1

The largest number possible with the digits 1-6 using each exactly once and the four basic arithmetic operations is 721, by organizing the digits into the expression 6 * 5 * (2 ^ 3) * (4^1).

The correct option is B.

Step-by-step explanation:

The largest number you can get by composing an arithmetic expression from the digits 1, 2, 3, 4, 5, and 6, using each digit exactly once, and using the signs of four arithmetic operations is 721. To achieve this, you can use the expression 6 / 1 * (5 + 4) * (3 * 2) which calculates as follows:

• 5 + 4 = 9
• 3 * 2 = 6
• 9 * 6 = 54
• 6 / 1 = 6
• 6 * 54 = 324

Combining all this gives us 6 / 1 * 9 * 6 = 6 * 54 = 324. However, this is not the end as we can factor in exponents to get a larger value. Considering 4 as an exponent to 3 and using remaining numbers, the expression becomes 6 * 5 * (2 ^ 3) * (4^1) giving us:

• 2 ^ 3 = 8
• 4^1 = 4
• 6 * 5 * 8 * 4 = 721

Hence, the correct answer is 721, so option b) is the correct choice.

The correct option is B.