Stingers

ALERT: THE MORE CORRECT ANSWERS YOU SUBMIT, THE MORE ENTRIES YOU HAVE IN EACH SEMESTER'S RAFFLE!

New/Unsolved Problems: Math Stinger #180
Suppose integers x, y, z form an arithmetic progression, and x, y+1, z+2026 form a geometric progression. Find, with explanation, the sum of the smallest three such x's.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #179
Between 1,000 and 1,000,000 inclusive, which are more numerous, those integers whose base-ten representations contain a "1" or those that do not? Explain your answer.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #178
A random pizza is made by flipping a fair coin to decide whether to include pepperoni, then doing the same for sausage, mushrooms, and onions. Find, with explanation, the probability that two random pizzas have at least one topping in common.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #177
Suppose P(x) is the polynomial of least degree with integer coefficients such that P(√3 - √2) = √3 + √2. Find P(2026) with explanation.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #176
How many ways are there to split the integers 1 through 20 into 10 pairs so that in each pair the greater number is at least 2 times the lesser number? Explain your answer.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #174
Find the area of the region satisfying |x+y| + |x| + |y| ≤ 2025 in the xy-plane. Explain your answer.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #172
Is it true that for any 5 points on the boundary of a circle, some 3 of them must form an obtuse triangle? How about some 3 of them must form an acute triangle? Explain your answers.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #169
Suppose f(x) is a continuous function from the interval [0, 2025] to the interval [0, 2025] and f(f(x)) = x for all x in [0, 2025]. Explain why f(x) has to be either a strictly increasing or a strictly decreasing function. 

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #168
There are finitely many points in the xy-plane. Suppose any 3 of these points form a triangle with area at most 1. Show that there is a rectangle of area 4 that encloses all these points. (Extra challenge: Can you reduce the number 4 to something smaller?)

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #165
Ten positive real numbers are written on a board. The sum of their pairwise products is 1. Can we cross out one number so that the sum of the remaining numbers is less than √2 ? Justify your answer. (Hint: Consider (x₂+x₃+...+x₁₀)². )

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #163
A 2023 survey found that U.S. teenagers spent an average of 4.8 hours on social media platforms every day, with girls spending an average of 5.3 hours compared to 4.4 hours for boys. Find the ratio of girls to boys who participated in the survey. Justify your answer.

Please send solutions to tchan4 at kennesaw dot edu

 

Math Stinger #154
A piece of paper is divided into four rectangles as shown below. It is clear that the one at the bottom-left corner has the largest area and the one at the top-right corner has the smallest area. Without making measurements, how can we decide which of the other two rectangles has the larger area?

Please send solutions to tchan4 at kennesaw dot edu.

 

Older Solved Stinger Problems (click here for questions and solutions)