Math Riddles
Number Theory
Combinatorics
Geometry
Algebra
100
What is 7 + 7 ÷ 7 + 7 x 7 – 7 ?
50
100
Find the largest integer less than 80 that leaves a remainder of 3 when divided by 5.
78
100
A test has four answer choices and four questions. In how many ways can you answer all the questions on the test?
256
100
Rectangle ABCD has AB = 6 and BC = 3. Point M is chosen on side AB so that ∠AMD = ∠CMD. What is the degree measure of ∠AMD?
75
100
x2 + 5x + 6 = 0 (both x values)
x = -2, -3
200
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years time, I will be twice as old as my brother.” How old are they each now?
One way to solve this math riddle is to use even numbers: The older brother will be twice as old as his younger brother in three years’ time. This immediately rules out the older brother currently being 8, 11 and 14, so he must be 17, and the younger brother 7. Two years ago, they were 15 and 5 respectively, and in three years, they will be 20 and 10.
200
What is the difference between the largest and the smallest prime factors of 462?
9
200
Compute 24C3 (24 choose 3).
2024
200
A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
5
200
Positive integers m and n satisfy lcm(m, n) = 210. What is the minimum possible value of m + n?
29
300
(0! + 0! + 0! + 0! + 0! + 0!)!
720
300
What is the smallest positive three-digit number that is a multiple of 4 and whose digits' sum is 23?
788
300
Harrison has 10 identical apples and 2 identical baskets. In how many ways can he put the apples into the baskets?
11
300
Six cubes, each an inch on an edge, are fastened to- together, as shown. Find the total surface area in square inches. Include the top, bottom, and sides.
26
300
Call a string of letters fearless if its first and last letters are the same. How many permutations of the letters in the word FEARLESS are fearless?
720
400
What single digit appears most frequently between and including the numbers 1 and 1,000?
The most common digit is 1! Did you figure out why? Every number 1–9 appears exactly the same number of times in every ten numbers. But because we included the number 1,000, there’s an extra occurrence of the number 1. In total, the number 1 appears 301 times, and every other number appears 300 times.
400
What is the largest integer that must divide the product of any 4 consecutive integers?
24
400
A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the male giraffe, how many ways can he feed all the animals?
144
400
The midpoints of the sides of a triangle with area 
are joined to form a triangle with area 
. What is the ratio of M to T? Express your answer as a common fraction.
1\4
400
9
500
John noticed that the amount he was paying for his lunch was a rearrangement of the digits of the amount of money he had in his pocket and that the money he had left over was yet another rearrangement of the same three digits! How much money did John start with?
John started with $9.54. The money can be written with just three digits, so it must be between $1.01 and $9.99. Trial and error shows that there is only one set of numbers that fits this question: $9.54 = $4.59 + $4.95.
500
What is the units digit of 
7
500
If the odds for pulling a prize out of the box are 3:4, what is the probability of not pulling the prize out of the box? Express your answer as a common fraction.
4/7
500
From point A, Leigh walked 40 yards south, 60 yards west, 10 yards north, and 20 yards east to point 
. What is the length, in yards, of 
?
50
500
Find the sum of product of the roots and the sum of the roots of x3-x2+3x+7.
-6