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You are given an 8×8 chess-board, and in each of its cells
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,
You throw me away.
But when you are done with me,
You bring me back.
What am I?
The answer is ANCHOR.
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
The kid suggested that the man uses one bolt from each of the other three wheels to fix the fourth one.
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?
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.
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?
The answer is KEY.
Prove that among any 9 points in (3D) space, there are three which form an obtuse angle.
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.
Get from START to END in this maze, created by Sean Jackson.
The solution is shown below.
The following is a riddle. Do not solve the riddle. Instead, explain the title.
My top is tilted to the light,
A trumpet, almost, in its form.
You court a woman? There I am.
I please, palliate, perfume and mourn.
Your grief I lament. Slay me and
I will you last amen adorn.
The riddle is about a (dismembered) flower. Its different parts are hidden within the words of the riddle:
My top is tilted to the light, -> pistil
A trumpet, almost in its form. -> petal
You court a woman? There I am. -> anther
I please, palliate, perfume and mourn. -> sepal
Your grief I lament. Slay me and -> filament
I will your last amen adorn. -> stamen
There are 100 passengers which are trying to get on a plane. The first passenger, however, has lost his boarding pass, so decides to sit on an arbitrary seat. Each successive passenger either sits on his own seat if it is empty or on an arbitrary other if it is taken. What is the chance that the last person will sit
The chance is 50%. Indeed, the last passenger will either have to sit in his own seat or the one which belongs to the first passenger. Since there hasn’t
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