Problem 28, Upper Primary: Australian Mathematics Competition 2023

Let's discuss a problem from the AMC 2023 Upper Primary: Problem 28 which revolves around basic calculation.

Problem

Using \(9\) out of the \(10\) possible digits Safia writes \(3\) numbers, each between \(100\) and \(999\). She adds her \(3\) numbers together. What is the smallest possible sum?

Solution

As mentioned the sum has to be the smallest possible so we have to consider the smallest numbers.

Let's select the three smallest numbers for the hundredth place: 1, 2, 3

Let's select the next three smallest numbers for the ten's place also include zero: 0, 4, 5
Let's select the next three numbers for the one's place: 6, 7, 8

Thus the three numbers become: \(106, 247, 358\)

If we add them the sum becomes: \(106 + 247 + 358 = 711 \).

Thus the smallest possible sum is \(711\).

What is AMC (Australian Mathematics Competition)?

The Australian Mathematics Competition (AMC) is one of Australia's largest and oldest annual mathematics competitions, aimed at fostering interest and excellence in mathematics among students.

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