UVU Math Challenge 2021

Pentomino Sudoku

This puzzle is a variation of Sudoku. A 10x10 grid is divided up into twenty five-block pentominoes. Each of these should contain the number 1-5. In addition, each row and column in the sudoku grid should contain each of the numbers 1-5 twice.

Download the puzzle here.

Submissions should be a scanned/photographed picture of your solution. A winner will be drawn at random from all correct solutions.

Function Fun

Suppose that f(x) is a function where

f(x+y) = f(x) + f(y) + xy

and

f(8) = 36,

find f(2021).

A winner will be drawn at random from all correct solutions.

Colorful Products

Suppose we have the numbers 1, 2, ..., n for some whole number n. We need to color each of these numbers in one of three colors: red, green, or blue. There is a rule for the coloring regarding products. Specifically, if a x b = c, where a, b, and c are different numbers, then

• the numbers a, b, and c cannot all be the same color, and

• the numbers a, b, and c cannot be three different colors.

(For example, the coloring 1 2 3 4 5 6 7 8 9 breaks two rules: 2 x 4 = 8 is a prohibited one-color product, and 2 x 3 = 6 is a prohibited three-color product. However, 2 x 2 = 4 isn't breaking the rules, because this product duplicates the number 2, so we're not considering it.)

What is the highest value of n so that 1, 2, ..., n can be colored according to these rules?

For this problem, the entry with the longest list that follows this rules will be declared the winner. Submit your list by downloading this file (link) and entering your numbers in the appropriate column. Ties will be broken by random draw.

Divide and Conquer

Let A be the set of all 6-digit numbers where the sum of the first three digits is equal to the sum of the last three digits. Let S be the sum of all the numbers in A. Show that S is divisible by 13.

A winner will be drawn at random from all correct solutions.

A winner will be drawn from all correct solutions.