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Problem of the week

Here are some fun, engaging math problems updated every week to help you engage yourself and improve your problem-solving skills and aptitude for math. This will also help prepare those who are competing in our competition as these problems are very similar in style and content. You can find last year’s highlighted problem’s of the week archived at the bottom of this page.

Problem #1

What is the largest possible prime divisor of every 3-digit number with three identical non-zero digits?

Problem #2

What is the greatest possible length of the longest side of
an isosceles triangle whose sides each have an integral length
whose perimeter is 5779?

Problem #3

Yossele’s coins consist of only pennies, nickels, dimes, and quarters. Yossele has less than 100 pennies and the total value of all of Yossele’s coins is $6.13. At most, how many pennies does he have?

Problem #4

If x and y are real numbers whose numbers whose sum is three times their product, and whose product is not 0. What is the value of x + y?

Problem #5

For all real numbers x, the function f is defined by f(x) = 5779. What is the value of f(x + 5779)?

Problem #6

Moshe runs three times as fast as he walks. It takes Moshe 21 minutes to get to work from home if he walks for twice the amount of the time he runs. How many minutes does it take Moshe to get to work from home if he runs for twice the amount of time that he walks?

Problem #7

Line J is perpendicular to lines m and n. If the product of the slopes of all 3 lines is -8, what is the slope of the line J?

Last Year’s Highlighted Problems of the Week

Here are the staff-picked favorites of last year’s problem of the week series as well as their corresponding answers and explanations. These will remain the same but this year’s series will be updated weekly with the new content so make sure to check back soon. Good luck!

Problem #1

Steve and Josh played a game. Steve wrote on a blackboard all integers from 1 to 18 and challenged Josh to choose 8 different integers from this list. To win the game Josh had to choose 8 integers so that among them the difference between any two of them is either less than 7 or greater than 11. Can Josh win the game? Justify your answer.

Problem #2

What is the smallest positive number k such that there are real numbers a and b satisfying
a + b = k and ab = k?

Problem #3

Patty is picking peppermints off a tree. They come in two colors, red and white. She picks fewer than 100 total peppermints but at least one of each color. The white flavor is stronger, so she prefers red to white. Thus, she always picks fewer white peppermints than ten times the number of reds. How many different combinations of peppermints can she go home with?

Problem #4

A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?

Problem #5

The sum of 5 real numbers is 8 and the sum of their squares is 16. What is the largest possible value for one of the numbers?

Problem #6

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son, and I together are 120 years. Can you tell me my age in years?

Problem #7

David, Steven, and Harry are going to the mall to buy clothes. 1/4 of David's money plus 1/4 of Steven's money is equal to 3 dollars. 1/5 of David's money plus 1/5 of Harry's money is equal to 2 dollars. If the sum of all their money is a multiple of 7 and they individually have whole number amounts of dollars, what are the possible values for David's money? (there may be more than one)

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