Puzzles
Maria went to the bread store to buy a loaf of bread for dinner. She had 2 quarters, 4 dimes, 3 nickels, and 2 pennies. The total cost of the bread is $0.82. She promised to make sure she had exactly 1 coin remaining after purchase. What coin did she have left after buying the loaf of bread?
One of the quarters.
Which of the following figures has the greatest number of lines of symmetry? Equilateral triangle, non-square rhombus, non-square rectangle, isosceles trapezoid, square
square
A board game spinner is divided into three regions labeled A, B, and C. The probability of the arrow stopping on region A is 1/3 and on region B is 1/2. What is the probability that it stops on region C?
1/6
What is the value of 4 times (-1+2-3+4-5+6-7+...+1000)?
2000
If the zookeeper had 100 pairs of animals in her zoo and if two pairs of babies are born for each and every one of the original animals, and then sadly 23 animals don’t survive, how many animals do you have left in total?
977 animals (100 x 2 = 200; 200 + 800 = 1000; 1000 – 23 = 977).
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone. Cassie says, 'I didn't get the lowest score in our class,' and Bridget adds, 'I didn't get the highest score.' What is the ranking of the three girls from highest to lowest?
Cassie, Hanna, Bridget
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?
6
You toss a nickel 4 times. What is the probability that you get at least as many heads as tails?
11/16
How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
9
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did the 6th player win?
2
A duck was given $9, a spider was given $36, a bee was given $27. If this pattern is continued, how much money would be given to a cat?
$18 ($4.50 per leg)
A 1x2 rectangle is inscribed in a semicircle with longer side on the diameter. What is the area of the semicircle?
pi
Two fair coins are to be tossed once. For each head that results, one fair die is to be rolled. What is the probability that the sum of the die rolls is odd? (Note that if no die is rolled, the sum is 0.)
3/8
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
3127
Both roots of the quadratic equation x^2 - 63x + k = 0 are prime numbers. How many possible values of k are there?
1
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble. It is a white marble. What is the probability that the remaining marble from the same bag is also white?
2/3
An equilateral triangle of side length 10 is completely filled in by non-overlapping equilateral triangles of side length 1. How many small triangles are required?
100
A bag contains only blue balls and green balls. There are 6 blue balls. If the probability of drawing a blue ball at random from this bag is 1/4, then what is the number of green balls in the bag?
18
What is the units digit of 13 to the 2023?
7
A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one?
18
How many steps are required to break an m × n sized bar of chocolate into 1 × 1 pieces? You can break an existing piece of chocolate horizontally or vertically. You cannot break two or more pieces at once (so no cutting through stacks). Give an answer in terms of m and n.
m x n - 1
Two points on the circumference of a circle of radius r are selected independently and at random. From each point a chord of length r is drawn in a clockwise direction. What is the probability that the two chords intersect?
1/3
Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers have a difference that is a multiple of 5?
1
For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?
4015
A frog sitting at point (1,2) begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length 1, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices (0,0), (0,4), (4,4), and (4,0). What is the probability that the sequence of jumps ends on a vertical side of the square?
5/8