Digit Power Sum
The number $512$ is interesting because it is equal to the sum of its digits raised to some power: $5 + 1 + 2 = 8$, and...
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John Rhodes
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August 15, 2023
Pandigital Prime Sets
Using all of the digits $1$ through $9$ and concatenating them freely to form decimal integers, different sets can be formed. Interestingly with the set $\{2,5,47,89,631\}$, all...
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John Rhodes
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August 15, 2023
Red, Green, and Blue Tiles
Using a combination of grey square tiles and oblong tiles chosen from: red tiles (measuring two units), green tiles (measuring three units), and blue tiles (measuring four...
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John Rhodes
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August 15, 2023
Red, Green or Blue Tiles
A row of five grey square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), green (length...
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John Rhodes
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August 15, 2023
Counting Block Combinations II
NOTE: This is a more difficult version of Problem 114. A row measuring $n$ units in length has red blocks with a minimum length of $m$ units...
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John Rhodes
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August 15, 2023
Counting Block Combinations I
A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red blocks (which...
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John Rhodes
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August 15, 2023
Non-bouncy Numbers
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, $134468$. Similarly if no digit...
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John Rhodes
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August 15, 2023
Bouncy Numbers
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, $134468$. Similarly if no digit...