Never in a Thousand Years
What occurs once in every minute, twice in every moment, but never in a thousand years?
SOLUTION
The answer is THE LETTER M.
Integers on a Chess Board
You are given an 8×8 chess-board, and in each of its cells
SOLUTION
Consider the intervals spanned by the numbers in the first row, second row, third row, etc. If all of these intervals intersect each other, then there is a number, which appears in all of them. If not, there are two intervals, which are disjoint, and a number between them, which does not appear in the two rows. Now it is easy to see that this particular number will appear in every column.
When You Need Me
When you need me,
You throw me away.
But when you are done with me,
You bring me back.
What am I?
SOLUTION
The answer is ANCHOR.
Deez Nuts
While changing a tire, a motorist accidentally dropped all four wheel nuts into the sewer grate. Just when the man lost all hope to retrieve the nuts and continue on his way, a kid passed by. After hearing the story, the kid gave an advice, which enabled the driver to successfully fit a new
SOLUTION
The kid suggested that the man uses one bolt from each of the other three wheels to fix the fourth one.
Game of Chess
Ned and Jon are playing chess. Eventually, they end up in a position in which Ned (whites) is left with 2 rooks, and Jon (blacks) has just his king on the board. If Ned can mate Jon in exactly 4 different ways, what is the position of the pieces?
SOLUTION
Black king on a1, white king on e1, white rooks on c2 and h1. Ned hasn’t moved his king and rook, so he can either castle or move his king to d2, e2 or f2, resulting in a mate.
Euclidea
Which was your favorite part of the Mathematics you
Riddle from Neverwhere
I turn my head, and you may go where you want.
I turn it again, and you’ll stay till you rot.
I have no face, but I live or die.
By my crooked teeth,
Who am I?
SOLUTION
The answer is KEY.
Obtuse Angle
Prove that among any 9 points in (3D) space, there are three which form an obtuse angle.
SOLUTION
Let the points be labeled A1, A2, … , A9, and P be their convex hull. If we assume that all angles among the points are not obtuse, then the interiors of the bodies P + A1, P + A2, … , P + A9 should be all disjoint. That is because, for every Ai and Aj, P must be bound between the planes passing through Ai and Aj which are orthogonal to the segment AiAj. However, all of these 9 bodies have the same volume and are contained in the body P + P, which has 8 times larger volume. This is a contradiction, and therefore our assumption is wrong.
The Golden Frog
Get from START to END in this maze, created by Sean Jackson.
SOLUTION
The solution is shown below.
