# Stingers

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

**New Problems: **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?

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?

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 Stinger Problems**

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 ak ≤ n?

Older solutions published to: Solved Stingers