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...
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John Rhodes
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August 15, 2023
Primes with Runs
Considering $4$-digit primes containing repeated digits it is clear that they cannot all be the same: $1111$ is divisible by $11$, $2222$ is divisible by $22$, and...
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John Rhodes
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August 15, 2023
Diophantine Reciprocals II
In the following equation $x$, $y$, and $n$ are positive integers. $$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{n}$$ It can be verified that when $n = 1260$ there are...
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John Rhodes
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August 15, 2023
Darts
In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty. The...