Two Sisters
Two sisters we are, one is dark and one is fair,
In twin towers dwelling we’re quite the pair,
One from land and one from sea,
Tell us truly, who are we?
SOLUTION
The answer is SALT AND PEPPER.
Category: Puzzles
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Hidden Objects Crowds
Can you find the objects hidden in the three pictures below? You are looking for:
- 1 panda among the heavy metal artists
- 1 panda among the storm troopers
- the Queen among her Corgies
SOLUTION
Coming soon.
0 > 2, 2 > 5, 5 > 0
0 > 2, 2 > 5, 5 > 0. What is this?
SOLUTION
This is the game “Rock, Paper, Scissors”. Rock (0 fingers) beats scissors (2 fingers). Scissors (2 fingers) beats paper (5 fingers). Paper (5 fingers) beats rock (0 fingers).
Cow and Rope
A cow is tied to a 4 meter long rope. There is food, 20 meters away from the cow. However, the cow manages to go to the food and eat it. How come?
SOLUTION
The rope is not tied to anything but the cow, so the cow is free to go to the food.
The Missing Digit
The number 229 has 9 digits, all different. Which digit is missing?
Bonus: Is the number 9991 prime?
SOLUTION
Let the missing digit be m. Every number and the sum of its digits give the same remainder when divided by 9. The number 229 = 32 * 644 gives remainder 5 when divided by 9, and therefore 9 divides (0 + 1 + 2 + … + 9) – 5 – m = 40 – m. Thus, the missing digit is 4.
Bonus: 9991 = 10000 – 9 = 1002 – 32 = (100 – 3)(100 + 3) = 97 * 103. Therefore the number 9991 is not prime.
Cover the Table
100 coins are placed on a rectangular table, such that no more coins can be added without overlapping. Show that you can cover the entire table with 400 coins (overlapping allowed).
SOLUTION
Since we can not place any more coins on the table, each point of it is at distance at most 2r from the center of some coin, where r is the radius of the coin. Now shrink the entire table twice in width and length, then replace every shrunk coin with a full sized one. This way the small table will be completely covered because every point of it will be at distance at most r from the center of some coin. Add three more of these smaller tables, covered with coins, to create a covering of the big table.
Borromean Rings
Borromean rings are rings in the 3-dimensional space, linked in such a way that if you cut any of the three rings, all of them will be unlinked (see the image below). Show that rigid circular Borromean rings cannot exist.
SOLUTION
Assume the opposite. Imagine the rings have zero thickness and reposition them in such a way, that two of them, say ring 1 and ring 2, touch each other in two points. These two rings lie either on a sphere or a plane which ring 3 must intersect in four points. However, this is impossible.
Slice My Head
You use a knife to slice my head,
And weep beside me when I’m dead.
What am I?
SOLUTION
The answer is ONION.
Puzzle Sum 21
What animal does this sum spell?
What fish does this sum spell?
SOLUTION
BAR + MUFF – ARM + BUS + HALO – BUSH = BUFFALO
SHAWL – AWL + ARK = SHARK
Seven Sevens
Seven sevens are given. Find the other digits in this multiplication.
SOLUTION
The answer is:
21817 x 96787 = 2111601979
