Math Problems for 2024

The calendar is about to change again, and another year of possibilities lies before us. While there are many things that you might do this year, I beg you, please, do not find the sum of all odd positive divisors of 2024. It’s two gross!

There are many interesting problems that involve the number 2024. Enjoy!

• A “multiplicative date” is one in which the product of the month and date is equal to the (two-digit) year. For instance, August 3 is a multiplicative date in 2024, because 8 × 3 = 24. How many multiplicative dates will there be in 2024?
• Create a polygon whose perimeter is 2024 units and whose area is 2024 square units.
• The sum of the digits of 2024 is 2 + 0 + 2 + 4 = 8, and 8 is a factor of 2024. For how many numbers in the 2020s is the sum of the digits a factor of the number?
• The number 2024 is an iban number, because the English name for the number “two-thousand twenty-four” never contains the letter i. (It has no relationship to the banking term IBAN, which stands for “International Bank Account Number.” It also only applies to the standard English names for numbers, not special names like googol or Kaprekar’s constant.) What is the largest iban number?
• What is the sum of 1 + 2 + 3 + 4 + ··· + 2024?
• What is the sum of 2 + 4 + 6 + 8 + ··· + 2024?
• What is the sum of 13 + 26 + 39 + ··· + 2024?
• How long would it take you to count to 2024?
• Using only common mathematical symbols and operations and the digits 2, 0, 2, and 4, make an expression that is exactly equal to 100. (Bonus: make an expression using the four digits in order.)
• All possible four-digit numbers that can be made with the digits 2, 0, 2, and 4 are formed and arranged in ascending order. What is the median of those numbers?
• What fraction is equivalent to 0.2024?
• How many positive integer factors does 2024 have?
• Create a 4 × 4 magic square in which the sum of each row, column, and diagonal is 2024.
• What is the units digit of 2024²⁰²⁴?
• Each dimension of a rectangular box is an integer number of inches. The volume of the box is 2024 in³. What is the minimum possible surface area of the box?
• What is the maximum possible product for a set of positive integers that have a sum of 2024?
• A polynomial p has non-negative integer coefficients and satisfies p(1) = 8, p(-1) = 0, and p(3/2) = 13.75. What is p(10)?
• Let S(n) denote the sum of the digits of integer n. For example, S(123) = 6. Find a number n such that n + S(n) + S(S(n)) + S(S(S(n))) = 2024.

Special thanks to Professor Harold Reiter for supplying the last two problems in the list.

[Update 12/31/23] Too beautiful not to share, this truth about the year was posted in the Wolfram Community by Ed Pegg of Wolfram Research:

2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ = 2024

And this representation appeared in a post about math beauties of the new year at Math 1089:

2024 = 1 − 2 + 3 × (4 + 5) × (6 + 78 − 9)

Awesome.