Gathering the Beans
Whenever Peter feels bored, he places some bowls, containing one bean each, in a circle. After this, he takes all the beans out of a certain bowl...
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John Rhodes
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August 15, 2023
Spilling the Beans
In Plato’s heaven, there exist an infinite number of bowls in a straight line. Each bowl either contains some or none of a finite number of beans....
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John Rhodes
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August 15, 2023
Special Partitions
All positive integers can be partitioned in such a way that each and every term of the partition can be expressed as $2^i \times 3^j$, where $i,j...
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John Rhodes
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August 15, 2023
Cross Flips
$N \times N$ disks are placed on a square game board. Each disk has a black side and white side. At each turn, you may choose a...
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John Rhodes
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August 15, 2023
Euler’s Number
An infinite sequence of real numbers $a(n)$ is defined for all integers $n$ as follows: $$a(n) = \begin{cases} 1 & n \lt 0\\ \sum \limits_{i = 1}^{\infty}{\dfrac{a(n...
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John Rhodes
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August 15, 2023
Prime Frog
Susan has a prime frog. Her frog is jumping around over $500$ squares numbered $1$ to $500$. He can only jump one square to the left or...
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John Rhodes
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August 15, 2023
Lowest-cost Search
We are trying to find a hidden number selected from the set of integers $\{1, 2, \dots, n\}$ by asking questions. Each number (question) we ask, has...
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John Rhodes
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August 15, 2023
Rooms of Doom
A series of three rooms are connected to each other by automatic doors. Each door is operated by a security card. Once you enter a room the...