Stingers
ALERT: THE MORE CORRECT ANSWERS YOU SUBMIT, THE MORE ENTRIES YOU HAVE IN EACH SEMESTER'S RAFFLE!
New/Unsolved Problems: Math Stinger #171
Solve log22025 + log42025 = logx2025.
Please send solutions to tchan4 at kennesaw dot edu
Math Stinger #170
Two positive real numbers have their sum less than their product. Prove that their
sum is greater than 4.
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 #167
Is it possible to partition the consecutive integers from 1 to 12 into several groups
such that, in each group, the largest number equals to the sum of the remaining numbers?
Justify your answer.
Please send solutions to tchan4 at kennesaw dot edu
Math Stinger #166
A fair coin is tossed 8 times. What is the probability that 3 heads appear in succession
somewhere along the sequence of tosses?
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 #164
Let ABC be an isosceles triangle with vertex angle A. Let E and D be points on AC
and AB so that AE = ED = DC = CB. Find angle A.
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 #162
For any prime number p > 5, consider the sequence p - 1, p - 4, p - 9, p - 16, . .
. . Is it true that there are two terms of this sequence, both greater than 1, such
that one divides the other? 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.
Math Stinger #153
There are 6 students, each has an item of gossip known only to himself/herself. Whenever
a student calls another, they exchange all items of gossip they know. What is the
minimal number of calls they have to make in order to ensure that very one of them
knows all the gossip there is to know? Justify your answer.
Please send solutions to tchan4 at kennesaw dot edu.
Older Solved Stinger Problems (click here for solutions)
Math Stinger #161
We have three cardboard isosceles right triangles of unequal sizes. No markings of
any kind are allowed. You may overlap the triangles. Is it possible to locate the
midpoint of the hypotenuse of the smallest triangle? How about the midpoint of the
non-hypotenuse side of the smallest triangle? Justify your answers.
Math Stinger #160
A fair coin is tossed eleven times. Find the probability that two heads do not appear
in succession.
Math Stinger #159
Find all positive integers which are one more than the sum of the squares of their
base ten digits. For example, 35 = 1 + 32 + 52.
Math Stinger #158
Is it possible to place four black unit circles and three white unit circles on the
plane so that the white circles cannot move to other positions while staying on the
plane, if the black circles are fixed in their position? Justify your answer.
Math Stinger #157
A strike force is to be selected from a row of eleven agents. It is known that three
of them have special abilities. It is not known who they are, except that they are
evenly spaced in the row. Find, with justification, the minimum number of agents we
need to pick so that at least one agent with special abilities is included.
Math Stinger #156
Your calculator is not working properly - it cannot perform multiplication. But it
can add and subtract any two numbers. It can also compute x-1 and x2 of any number x. Can you nevertheless use this defective calculator to multiply two
numbers?
Math Stinger #155
In a math class, 21% of the students get an A and 81% of those A students are part-time
students. Among part-time students, 31% of them do not get an A. What percentage of
the whole class are part-time students?
Math Stinger #152
Without using any calculator or computer, determine (with justification) which of
the following two quantities 1.0000000001 + 1 / 1.0000000001 or 0.9999999999 + 1 /
0.9999999999 is bigger?
Math Stinger #151
Going at top speed, Grand Prix driver x leads his rival y by a steady three miles.
Only two miles from the finish, x runs out of fuel. Thereafter x's deceleration
is proportional to the square of his remaining velocity, and, in the next mile, his
speed exactly halves. Who wins, and why?
Math Stinger #150
Let us assume that a given pair of people either know each other or are strangers.
If six people enter a room, show that there must be either three people who know
each other pairwise or three people who are pairwise strangers.
Math Stinger #148
For two given positive integers n and k, how many different sequences of positive
integers a1 ≤ a2 ≤ a3 ≤ ... ≤ ak are there in which ak ≤ n?
Older solutions published to: Solved Stingers
