Impossible Mate
White to move and mate Black.
SOLUTION
Coming soon.
Unknown Author
We do not know where this puzzle originated from. If you have any information, please let us know via email.
We do not know where this puzzle originated from. If you have any information, please let us know via email.
Tie a Knot
First, get a completely untangled rope. Now, your task is to grab its two ends, and without letting it go, tie this knot in the middle.
SOLUTION
In order to do this, first cross your arms, and from this position, grab the two ends of the rope. Once you untangle your arms, the knot will appear on the rope.
When You Have Me
When you have me, you want to share me.
When you share me, you no longer have me.
SOLUTION
The answer is SECRET.
Donuts and Candies
Huey has 3 donuts, Dewey has 5 donuts. Louie comes along and the three of them split the donuts equally. In exchange, Louie offers 8 candies to Huey and Dewey. What is the fair way to split the candies?
SOLUTION
Huey must take 1 chocolate, and Dewey must take 7. This is because each of them ate 8/3 donuts, and therefore Huey gave away 1/3 of a donut, whereas Dewey gave away 7/3 of a donut.
Inside Outside
You throw away the outside and cook the inside. Then you eat the outside and throw away the inside. What do you eat?
SOLUTION
The answer is CORN.
False Statements
None of these statements is correct.
At most 1 of these statements is correct.
At most 2 of these statements are correct.
…
At most 98 of these statements are correct.
At most 99 of these statements are correct.
How many of these statements are correct?
SOLUTION
If the number of true statements is X, then statements 1, 2, … , X are wrong, and the rest are correct. Therefore X = 100 – X and X = 50. Thus, there are 50 correct statements.
Mastermind
You must find a 3-digit number. You know that:
- 682 shares one digit with the number, and it is well placed;
- 614 shares one digit with the number, but it is wrongly placed;
- 296 shares two digits with the number, but they are wrongly placed.
What is the number?
SOLUTION
The first and second clues imply that the 6 is not a part of the number. The third clue then implies that 2 and 9 are parts of the number. Now the first clue implies that 2 is the last digit of the number, and the third clue implies that 9 is the first digit of the number. Finally, the second clue implies that 4 is the second digit of the number. Therefore, the number is 942.
Islands and Bridges
You need to cross a river, from the north shore to the south shore, via a series of 13 bridges and six islands, which you can see in the diagram below. However, as you approach the water, a hurricane passes and destroys some (possibly none/all) of the bridges. If the probability that each bridge gets destroyed is 50%, independently of the others, what is the chance that you will be able to cross the river after all?
SOLUTION
Imagine there is a captain on a ship, who wants to sail through the river from West to East. You can see that he will be able to do this if and only if you are not able to cross the river. However, if you rotate the diagram by 90 degrees, you can also see that the probability that you cross North-South is equal to the probability that he sails West-East, and therefore both probabilities are equal to 50%.
Every Acute Triangle
Consider an arbitrary acute triangle ABC. Let E be the intersection of the bisector at vertex C and the bisection of the side AB. Let F and G be the projections of E on AC and BC respectively.
Since E belongs to the bisection of AB, we must have AE = BE. Also, since E belongs to the bisector of C, we must have EF = EG. However, this would imply that triangles AEF and BGF are identical, and then AF = BF. We also have that CF = CG, which implies that AC = BC. The arbitrarily chosen triangle ABC is isosceles!
Can you find where the logic fails?
SOLUTION
The bisector of C and the bisection of AB always intersect outside the triangle, on the circumcircle. One of the points F and G always lies on the segment AC or BC, and the other one does not.
Erica, Tina, and Mark
If Erica lives in New York and Tina lives in Buenos Aires, where does Mark live?
SOLUTION
New York is the largest city in the United States of Am-Erica. Buenos Aires is the largest city of Argen-Tina. Therefore Mark lives in Den-Mark’s largest city – Copenhagen.