The answer is 2025 but what is the question?

You can be a creative mathematician, you can be someone who has your own mathematical ideas. Find your own interesting facts about the number 2025 and calculations that have the answer 2025.

For example, you might ask:  ‘do you find anything interesting if you reverse the digits of 2025 and add the two numbers together?’

Or you might ask: ‘what are the prime factors of 2025?’ or ‘Is it a square number?’ or ‘How many divisors of 2025 are there?’

What different questions can you find with 2025 as the answer?

The sum of the first n odd numbers is S_n= n² so 2025 is the sum of the first 45 odd numbers. Check it out! 1 + 3 + 5 + 7 + 9 + …+ 89 = 2025.

You might like to investigate powers of whole numbers. Can 2025 be written as the sum of squares or as the sum of cubes? For example you might ask: ‘What is $1^3 + 2^3 + 3^3 +4^3 +5^3 +6^3 +7^3 +8^3 +9^3?’$

You might ask ‘is 2025 a polite number or another sort of special number?’  A number is said to be polite if it can be expressed as the sum of at least two consecutive natural numbers. The number 2025 is a polite number since it can be written in 14 ways as a sum of consecutive natural numbers, for example, 403 + 404 + 405 + 406 + 407 = 2025. Can you find all 14 sums of consecutive numbers adding up to 2025?

What is the number 2025 written as a binary number?

How many ways can you arrange the digits 2, 0, 2  and 5 to get different numbers? What is the sum of those numbers?

Perhaps you can make up an easy question, one that is harder and one that is very hard.

Compare your questions with other people’s.

Is it correct to say “twenty twenty-five” or should we say “two thousand and twenty-five” or are both correct?  Why?

People say “twenty twenty five” so do the 2 twenties mean – 20 thousands, 20 hundreds, 20 tens or 20 units?

What interesting facts can you find about the year that you were born?

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