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I have three numbers, and the product of any two of the numbers is equal to the other remaining number: abbcca=c=a=b. Is it true that the three numbers must be either all 0s or all 1s?
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It is possible to arrange four copies of an equilateral triangle to cover an equilateral triangle with twice its side length. The same holds for a square:
However, doing the same exercise with a regular polygon with more sides requires some overlapping:
Covering a regular pentagon with double the side length requires 6 pentagons
How many identical regular hexagons are needed to cover a regular hexagon with double the side length?
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If I randomly pick a card from the ten above (ace = 1), then the probability of it having an odd number or an even number is equal.
If I instead randomly pick two distinct cards from the ten above, is the probability of the two numbers having an odd sum or an even sum still equal?
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A doctor soaks a cast with body-temperature water and wraps it around a patient’s arm. As the cast begins to set, does the patient feel a difference in temperature?
Note: This is a hydration reaction. As the cast hardens, water molecules "attach themselves" to the cast.
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Magnus, Garry, and Fabiano are playing in an exhibition badminton event. In this exhibition, after two players face off for a set, the winner of the set stays on the court to play the player who was sitting out.
At the end of the event, Magnus has played 9 sets, Garry has played 14 sets, and Fabiano has played 15 sets.
What pair played set number 13?
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