Square Digit Chains
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before....
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John Rhodes
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August 15, 2023
Right Triangles with Integer Coordinates
The points $P(x_1, y_1)$ and $Q(x_2, y_2)$ are plotted at integer co-ordinates and are joined to the origin, $O(0,0)$, to form $\triangle OPQ$. There are exactly fourteen...
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John Rhodes
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August 15, 2023
Cube Digit Pairs
Each of the six faces on a cube has a different digit ($0$ to $9$) written on it; the same is done to a second cube. By...
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John Rhodes
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August 15, 2023
Roman Numerals
For a number written in Roman numerals to be considered valid there are basic rules which must be followed. Even though the rules allow some numbers to...
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John Rhodes
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August 15, 2023
Product-sum Numbers
A natural number, $N$, that can be written as the sum and product of a given set of at least two natural numbers, $\{a_1, a_2, \dots, a_k\}$...
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John Rhodes
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August 15, 2023
Prime Power Triples
The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is $28$. In fact, there are exactly four numbers below...
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John Rhodes
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August 15, 2023
Cuboid Route
A spider, S, sits in one corner of a cuboid room, measuring $6$ by $5$ by $3$, and a fly, F, sits in the opposite corner. By...
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John Rhodes
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August 15, 2023
Counting Rectangles
By counting carefully it can be seen that a rectangular grid measuring $3$ by $2$ contains eighteen rectangles: Although there exists no rectangular grid that contains exactly...