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A regular hexagon is split into small equilateral triangles and then the triangles are paired arbitrarily into rhombuses. Show that this results into three types of rhombuses based on orientation, with equal number of rhombuses from each type.

Color the rhombuses based on their type and imagine the diagram represents a structure of small cubes arranged in a larger cube. If you look at the large cube from three different angles, you will see exactly the three types of rhombuses on the diagram.

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Rearrange the eight queens so that no two of them attack each other. For an extra challenge, make sure that no three of them lie on a straight line.

The original puzzle has 10 unique solutions, up to rotation and symmetry. With the additional restriction imposed, there is only one solution.

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David Justice and Derek Jeter were professional baseball players. In 1997 they had the following conversation:

David: Did you know that in both 1995 and 1996 I had better batting averages than you?

Derek: No way, my batting average over the last two years was definitely higher than yours!

It turned out that both of them were right. How is it possible?

This is the so called Simpson’s paradox. The reason it occurred is that during 1996 both players had high averages and Derek Jeter had many more hits than David Justice. In 1996 both players had low averages and David Justice had many more hits than Derek Jeter. You can see their official statistics below.

Player199519961995-1996
Derek Jeter12/48 (.250)183/582 (.314)
195/630 (.310)
David Justice104/411 (.253)45/140 (.321)149/551 (.270)
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There is a common 9-letter word in the English language, such that if you keep removing its letters one by one, the resulting 8 words are still valid. What is this word?

Remark: The removed letters do not need to be from the beginning or the end of the word.

The word is STARTLING -> STARTING -> STARING -> STRING -> STING -> SING -> SIN -> IN -> I.

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These are a few enigmas from the puzzle book CODEX ENIGMATUM. What is the answer to puzzle #9?

You can buy the complete book, created by Rami Hansenne, from this LINK.

  • Puzzle #2 After turning the first wheel 22 times to the right, then 19 times to the left, then 15 times to the right, and finally 11 times to the left, the final wheel will spell the word EXIT.
  • Puzzle #3 The total number of spots on the hidden sides of the die on the left is 6, which corresponds to the sixth letter in the alphabet – F. Therefore, the four dice on the right correspond to the letters K, I, N, G.
  • Puzzle #4 In the mosaic on the right, you can find a little star which contains pieces with letters H, I, D, E.
  • Puzzle #6 If you trace the signature on the paper, starting from the large C, you will pass through the letters C, O, N, T, I, N, U, O, U, S.
  • Puzzle #8 The picture on the left and the answer to puzzle #6 (“continuous”) suggest that we have to consider the images on the right which can be drawn continuously, without taking off the pencil from the paper or passing through any segment twice. These images are labeled with the letters N, O, S, E.
  • Puzzle #9 The first 2 letters from the word NOSE spell NO. The last letter from the word EXIT is T. The first letter from the word HIDE is H. The last three letters from the word KING spell ING. When you combine all of them, you get the word NOTHING.

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One person went to the store and bought groceries for $13.59 total. He paid with a $100 bill, took his change, and left the store. There was something special about this transaction. What is it?

The person paid with a $100 bill. The cashier returned him a $50 bill, a $20 bill, a $10 bill, a $5 bill, a $1 bill, a quarter, a dime, a nickel, and a cent. The transaction consisted of exactly one of each (frequently used) denominations.