Super Hard Riddles With Answers
Updated · Best Riddles With Answers editorial team
Quick answer: Super hard riddles ask for more than a clever guess. These 42 puzzles with answers are built on arithmetic, probability and step-by-step deduction, and every solution shows its working so you can check it. Keep a pencil handy, start with the warm-up set, and give the toughest ten at least ten minutes each.
Warm-Up Super Hard Riddles
A farm has cows and chickens. Counting heads gives 30 and counting legs gives 74. How many cows are there?
7 cows and 23 chickens. If all 30 were chickens there would be 60 legs, and each cow adds 2 more, so 14 extra legs means 7 cows.
Three boxes are labelled Apples, Oranges and Mixed, but every label is wrong. You may take one fruit from one box. Which box do you pick from to fix all labels?
The box labelled Mixed. Its fruit shows its true content, and the other two labels follow because each must be wrong.
I am a four digit number. My first digit is a third of my second, my third digit is the sum of my first two, and my last digit is three times my second. What number am I?
1349. The first digit a gives 3a, 4a and 9a for the others, and only a = 1 keeps every digit below ten.
A ship has a ladder over its side with ten rungs one foot apart, and the bottom rung touches the water. The tide rises one foot every hour. After two hours how many rungs are underwater?
None, because the ship rises with the tide, so the water stays at the bottom rung.
Two numbers add up to 20 and multiply to 96. What are they?
8 and 12, because 8 + 12 = 20 and 8 x 12 = 96.
Two numbers differ by 4 and multiply to 77. What are they?
7 and 11, because 11 - 7 = 4 and 7 x 11 = 77.
What number comes next: 1, 4, 10, 22, 46?
94. The gaps double: 3, 6, 12, 24, so the next gap is 48.
What number comes next: 3, 6, 11, 18, 27?
38. The gaps grow by 2: 3, 5, 7, 9, and the next gap is 11.
Which letter comes next: A, E, F, H, I, K, L, M, N?
T. These are the capital letters made only of straight lines, in alphabetical order.
What is the angle between the hands of a clock at 3:15?
7.5 degrees. The minute hand is at 90 degrees and the hour hand has moved a quarter of the way past 3, to 97.5 degrees.
How many squares of all sizes are there on a standard 8 by 8 chessboard?
204, because 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204.
How many rectangles of all sizes can you find in a 3 by 3 grid of squares?
36. Choose 2 of the 4 vertical lines and 2 of the 4 horizontal lines: 6 x 6 = 36.
Main Set Super Hard Riddles
Cheryl's birthday is one of: May 15, 16 or 19; June 17 or 18; July 14 or 16; August 14, 15 or 17. Albert is told the month and Bernard the day. Albert says, 'I don't know it, and I know Bernard doesn't either.' Bernard says, 'Now I know.' Albert says, 'Now I know too.' When is it?
July 16. Albert's remark removes May and June, Bernard's removes the 14th, and then only July has one date left.
A man says his three daughters' ages multiply to 36, and the sum equals the number on the house next door, which is 13. He adds that the oldest plays piano. What are their ages?
2, 2 and 9. Only 1, 6, 6 and 2, 2, 9 sum to 13, and only the second has a single oldest daughter.
A family has two children and at least one is a boy. What is the chance that both are boys?
One in three. The equally likely pairs are boy-boy, boy-girl and girl-boy, and only one has two boys.
A bag holds 2 red and 2 blue marbles. You draw two without looking. What is the chance they are the same colour?
One in three. There are 6 possible pairs, and 2 of them (both red or both blue) match.
A train leaves at 9:00 going 60 miles per hour. A second train leaves the same station at 10:00 on the same track going 80 miles per hour. When does the second train catch the first?
At 1:00 pm. The first has a 60 mile lead and the second gains 20 miles per hour, which takes 3 hours.
You drive to the city at 60 miles per hour and return the same way at 40 miles per hour. What is your average speed?
48 miles per hour. For a distance d, the time is d/60 + d/40 = d/24, and the total distance 2d divided by d/24 is 48.
What is the smallest number that is 1 more than a multiple of 2, 3, 4, 5 and 6, and is also a multiple of 7?
301. Numbers that are 1 more than a multiple of 60 are 61, 121, 181, 241 and 301, and only 301 is divisible by 7 (7 x 43).
I am a ten digit number. My first digit tells how many zeros there are in me, my second how many ones, my third how many twos, and so on through to my last digit, which counts nines. What number am I?
6210001000. It has six zeros, two ones, one two and one six.
A traveller must pay a hotel one link of a 7 link gold chain each night for 7 nights, with a single cut allowed. How does he do it?
Cut the third link, leaving pieces of 1, 2 and 4 links. Those make every total from 1 to 7 through swaps each night.
Split 10 into whole numbers that add to 10. What is the largest product you can make with them?
36, from 3 x 3 x 2 x 2 (3 x 3 x 4 also gives 36). Parts of 2s and 3s beat everything else.
What is the last digit of 7 multiplied by itself 100 times?
1. The last digits repeat 7, 9, 3, 1, and 100 is a multiple of 4.
In a race of 100 metres, Ana beats Ben by 10 metres. Ben beats Cat by 10 metres in a race of the same length. If Ana and Cat race, by how far does Ana win?
19 metres. When Ana finishes, Ben has run 90, and Cat has run 90 percent of that, which is 81.
Toughest Super Hard Riddles
You have twelve coins that look identical, but one has a different weight, heavier or lighter, and you do not know which. What is the fewest weighings on a balance scale that always finds it?
Three. Two weighings give only 9 outcomes, which cannot cover the 24 possibilities, but three give 27 and a careful plan reaches the answer.
Forty-one people stand in a circle numbered 1 to 41. Person 1 is skipped, person 2 is removed, then every second remaining person is removed and counting continues round. Who is the last one left?
Person 19. With n = 32 + 9, the survivor is 2 x 9 + 1 = 19.
A rectangular cake has a rectangular piece cut out of it from any place. How can one straight cut split what is left into two equal halves?
Cut through the centre of the whole cake and the centre of the missing piece. Both rectangles are halved by that line.
How many zeros are at the end of 50 factorial, the product of every whole number from 1 to 50?
12. Count factors of 5: 10 multiples of 5 plus 2 multiples of 25 gives 12.
The proper divisors of 6 (1, 2 and 3) add up to 6. What is the next number with this property?
28, because 1 + 2 + 4 + 7 + 14 = 28.
In SEND + MORE = MONEY, each letter is a different digit. What are the numbers?
9567 + 1085 = 10652. M must be 1, then O is 0, and the rest follow from the columns.
Tie a rope tightly around the Earth at the equator, then add one metre of rope and hold it evenly off the ground all the way round. About how large is the gap?
About 16 centimetres. The gap is 1 / (2 x pi) metres, whatever the size of the sphere.
What is the total of all the digits you write when you list the numbers from 1 to 100?
901. For 1 to 99 the digit sums add up to 450 for tens plus 450 for units, and 100 adds 1.
In TWO + TWO = FOUR each letter is a different digit. Find the sum.
734 + 734 = 1468. T = 7, W = 3, O = 4, F = 1, U = 6, R = 8.
How many three digit whole numbers have digits that add up to exactly 3?
Six: 102, 111, 120, 210, 300 and 201. List them by the first digit, which can only be 1, 2 or 3.
Quick-Fire Super Hard Riddles
What is the first prime number after 89?
97.
Which two digit number looks prime but is 7 times 13?
91.
What is half of two plus two?
Three.
What is the smallest number with exactly three divisors?
Four (1, 2 and 4).
What is the only even prime number?
Two.
Which number between 2 and 100 is both a perfect square and a perfect cube?
64.
What is zero factorial?
One.
What is the binary number 1010 in ordinary numbers?
Ten.
How to Approach Super Hard Riddles
Most super hard riddles reward a method more than a flash of insight. Write down what you know, name the unknowns, and test small cases. A pattern that holds for three or four items often reveals the rule. When a puzzle has several people or objects, draw a table and fill in what each clue rules out.
Check your answer against every statement in the question before you look at the solution. If it fails, find which clue it breaks and adjust. After each puzzle, read the explanation even when you were right, because the same technique tends to return in other puzzles.
Frequently Asked Questions
What is the hardest riddle with a real answer?
Hardness depends on the person, but puzzles such as the twelve coins, the circle of forty-one people and Cheryl's birthday are famous for needing careful reasoning. Each of them has a definite, checkable answer.
Do I need advanced maths for these riddles?
No. You need arithmetic, patience and careful reading. Techniques such as listing cases, working backwards and testing small examples are enough for every puzzle on this page.
How long should I spend on a super hard riddle?
Try for ten minutes with paper before looking at the answer. If you are stuck, read only the first sentence of the solution, then try again. Learning the method is worth more than a fast answer.
Are the answers on this page checked?
Yes. Every puzzle has a short explanation so you can verify the working yourself, including the arithmetic. If you ever find a different answer that fits every clue, test it against the question again.
