# Stingers

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

**New/Unsolved Problems: **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 #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.

Please send solutions to tchan4 at kennesaw dot edu

Math Stinger #160

A fair coin is tossed eleven times. Find the probability that two heads do not appear
in succession.

Please send solutions to tchan4 at kennesaw dot edu

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 + 3^{2} + 5^{2}.

Please send solutions to tchan4 at kennesaw dot edu

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.

Please send solutions to tchan4 at kennesaw dot edu.

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 x^{2} of any number x. Can you nevertheless use this defective calculator to multiply two
numbers?

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 #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 #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 a_{1} ≤ a_{2} ≤ a_{3} ≤ ... ≤ a_{k} are there in which a_{k} ≤ n?

Older solutions published to: Solved Stingers