Puzzles of logic are one of the best ways to measure your intelligence, quick wits and ability to think outside the box. The following selection of riddles, brain-teasers and numeric sequences are designed to separate the deep thinkers from the dunces. They start off easy and get progressively harder — best grab a pen and paper!
The following puzzles range from a popular maths exam question that an estimated 90% of students fail to get right to the self-proclaimed hardest logic puzzle in the world. If you manage to ace all of these you're either a borderline genius or a puzzle addict with a very good memory. We'll be updating the article with complete solutions next week. In the meantime, take your best stab in the comments!
“A watched pot never boils unless it is watched.” Is this statement true or false?
#2 Family Matters
A man was looking at a portrait when a passerby asked him, “Whose picture are you looking at?” The man replied: “Brothers and sisters have I none, but this man’s father is my father’s son.”
Whose picture was the man looking at?
Suppose, in the above situation, the man had instead answered: “Brothers and sisters have I none, but this man’s son is my father’s son.”
Now whose picture is the man looking at?
#3 There's a Star Hiding in This Image. Can You Find It?
Some of you will spot it quickly. Others of you will not.
#4 Six Matches, Four Triangles
Using six matchsticks of equal length, create four identical, equilateral triangles. (There's no need for snapping, burning, or otherwise altering the matchsticks.)
#5 Blowin’ in the Wind
An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less, or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?
#6 The Monk And The Mountain
At precisely 7:00 a.m., a monk sets out to climb a tall mountain, so that he might visit a temple at its peak. The trail he walks is narrow and winding, but it is the only way to reach the summit. As he ascends the mountain, the monk walks the path at varying speeds. Though he stops occasionally to rest and eat, he never strays from the path, and he never walks backwards. At exactly 7:00 p.m., the monk reaches the temple at the summit, where he stays the night.
The following morning at 7:00 a.m. sharp, the monk departs the temple and begins his journey back to the bottom of the mountain. He descends by way of the same path, again walking slowly at times and quickly at others, stopping here and there to eat and drink and rest, but never deviating from the path and never going backwards. Twelve hours later, at 7:00 p.m. on the nose, the monk arrives back at the foot of the mountain.
Is there any point along the path that the monk occupied at precisely the same time on both days? How do you know?
#7 Links in a Chain
The task: Join the four three-link chains on the left to form the circular chain on the right. To join two chains, you must cut, and then re-weld, a link. What is the minimum number of links you must cut and re-weld to complete the circle?
#8 Car park numbers
Can you explain the numbering system in this parking lot? What number is the parked car obscuring?
#9 Newton’s Trees
How can nine trees be arranged in ten rows, such that each row contains exactly three trees?
#10 Complete the series
Hint: The answer to this riddle is not "6".
#11 String Around the Rod
Twenty years ago, this puzzle appeared on a test administered to top-tier math students from 16 countries around the world. Apparently, only 10% of test takers got it right. Can you find the “simple” solution that so many intelligent students missed?
#12 Just the two of us
You and a fellow traveler are caught trespassing through the kingdom of the fear-instilling Mad King. As a punishment, the king imprisons you both in separate cells and presents you with a riddle, which you must solve correctly in order to save your lives.
“From your separate cells, you can each see half the land of my kingdom,” says the king, “across which are distributed either 10 or 13 villages. Each day at 5 p.m., I will give each of you an opportunity to tell me the number of villages in my kingdom. If your answer is correct, you will both be freed. But if your answer is wrong, you will both be killed.”
On the fifth day, the two of you are freed. How many villages are there in the king’s kingdom, and how many villages did you each see? How do you know?
#13 In Search of an Unusual Book
In a certain library, no two books contain the same number of words, and the total number of books is greater than number of words in the largest book.
How many words does one of the books contain, and what is the book about?
Need a hint? Here’s a conceptually similar puzzle, the answer to which can help put you in the right frame of mind for tackling this problem:
Why must there certainly be at least two people in the world with exactly the same number of hairs on their head?
#14 Counting Coins
You are blindfolded and brought to a table, on which rest fifty coins. Sixteen of them, you are told, are heads up. Thirty-four of them are tails up. Your task is to sort the coins into two groups, such that each group contains the same number of coins that are heads up. With your blindfold on, you cannot see if a coin is heads up. Neither can you feel a coin to determine its orientation. You can, however, move the coins and flip any number of them over.
#15 Potato Dryer
You have 100kg of potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?
#16 Pigs in pens
How can you distribute all 21 of your pigs into four pigpens and still have an odd number of pigs in each pen? You may place the same number of pigs in any number of pens (for example, the first and third pens can both contain 3 pigs), but the number of pigs in each pen must be odd. How do you distribute your pigs?
#17 The Perilous Bridge-Crossing
Four people fleeing a fire come to a river in the night. Spanning the river is a narrow bridge, which they must cross to safety before they are consumed by the fire.
The bridge is narrow and ill-kept, and can therefore support just two people at any one time. The four people share but one dim torch, which they must use to traverse the dilapidated bridge safely. Anyone who attempts a crossing without the torch is as good as dead.
All four people are injured in different ways, and so it takes them different amounts of time to cross the bridge. Person A can cross the bridge in one minute, person B in two minutes, person C in five minutes, and person D in ten minutes. When two people cross together, they must do so at the slower person’s pace.
With the fire growing closer by the minute, time is of the essence. What is the fastest time in which all four people can cross the bridge to safety?
#18 Buttered toast
Consider the preparation of three slices of hot buttered toast. The toaster is the old-fashioned type, with hinged doors on its two sides. It holds two pieces of bread at once but toasts each of them on one side only. To toast both sides it is necessary to open the doors and reverse the slices.
It takes three seconds to put a slice of bread into the toaster, three seconds to take it out, and three seconds to reverse a slice without removing it. Both hands are required for each of these operations, which means that it is not possible to put in, take out, or turn two slices simultaneously. Nor is it possible to butter a slice while another slice is being put into the toaster, turned, or taken out. The toasting time for one side of a piece of bread is thirty seconds. It takes twelve seconds to butter a slice.
Each slice is buttered on one side only. No side may be buttered until it has been toasted. A slice toasted and buttered on one side may be returned to the toaster for toasting on its other side. The toaster is warmed up at the start. In how short a time can three slices of bread be toasted on both sides and buttered?
#19 A Devious Selection Task
On the table before you are the above four cards. Your task is to turn over as few cards as possible to verify whether the following statement is true: Every card with a vowel on one side has an even number on the other side. You must decide in advance which cards you will examine.
#20 Three Boxes, Two Lies
The Fair Maiden Rowena wishes to wed. And her father, the Evil King Berman, has devised a way to drive off suitors. He has a little quiz for them, and here it is. It's very simple:
Three boxes sit on a table. The first is made of gold, the second is made of silver, and the third is made of lead. Inside one of these boxes is a picture of the fair Rowena. It is the job of the White Knight to figure out – without opening them – which one has her picture.
Now, to assist him in this endeavor there is an inscription on each of the boxes. The gold box says, "Rowena's picture is in this box." The silver box says, "The picture is not in this box." The lead box says, "The picture is not in the gold box." Only one of the statements is true. Which box holds the picture?
#21 100 green-eyed dragons
You visit a remote desert island inhabited by one hundred very friendly dragons, all of whom have green eyes. They haven't seen a human for many centuries and are very excited about your visit. They show you around their island and tell you all about their dragon way of life (dragons can talk, of course).
They seem to be quite normal, as far as dragons go, but then you find out something rather odd. They have a rule on the island which states that if a dragon ever finds out that he/she has green eyes, then at precisely midnight on the day of this discovery, he/she must relinquish all dragon powers and transform into a long-tailed sparrow. However, there are no mirrors on the island, and they never talk about eye color, so the dragons have been living in blissful ignorance throughout the ages.
Upon your departure, all the dragons get together to see you off, and in a tearful farewell you thank them for being such hospitable dragons. Then you decide to tell them something that they all already know (for each can see the colors of the eyes of the other dragons). You tell them all that at least one of them has green eyes. Then you leave, not thinking of the consequences (if any). Assuming that the dragons are (of course) infallibly logical, what happens?
If something interesting does happen, what exactly is the new information that you gave the dragons?
These puzzles were originally compiled by Robbie Gonzalez for iO9.