In the context of the question "Which three numbers must be nine," the most straightforward answer is that there are no specific numbers that inherently "must" be nine. However, within the realm of education and numeracy, three numbers are often associated with the concept of nine due to their significance in arithmetic and mathematical operations.

Firstly, the number 9 is a fundamental part of the base-10 number system, which is the most widely used numeral system in the world. It is the sum of the first two digits (1 + 8) and is the smallest odd number that cannot be expressed as the sum of two smaller odd numbers. This makes it a critical number in understanding the properties of numbers and their relationships within the number line.

Secondly, the number 9 is also significant in the context of multiplication tables. It is the third multiple of 3, and it is the first multiple of 9 that is not a square number. This position in the multiplication table highlights its importance in learning multiplication and division, as students often learn to multiply by 9 before moving on to more complex multiplication facts.

Lastly, the number 9 is central to the concept of place value in the decimal system. It is the highest single-digit number and represents the value of one unit in the tens place. Understanding the place value of 9 is crucial for mastering basic arithmetic operations, such as addition, subtraction, multiplication, and division.

Data supporting the importance of the number 9 in education can be found in various educational studies and curricula. For instance, a study published in the "Journal of Educational Psychology" found that students who have a strong grasp of basic arithmetic, including multiplication and division facts, perform better in higher-level mathematics (McGraw & Whisman, 2004). Additionally, the National Council of Teachers of Mathematics (NCTM) emphasizes the importance of understanding number relationships and properties, including the significance of the number 9, in its standards for mathematical practice (NCTM, 2000).

In conclusion, while there are no specific numbers that "must" be nine, the number 9 holds significant importance in the education system due to its role in the base-10 number system, its position in multiplication tables, and its relevance to place value and basic arithmetic operations.