Monopoly Odds
In the game, Monopoly, the standard board is set up in the following way: A player starts on the GO square and adds the scores on two...
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John Rhodes
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August 15, 2023
Path Sum: Four Ways
NOTE: This problem is a significantly more challenging version of Problem 81. In the $5$ by $5$ matrix below, the minimal path sum from the top left...
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John Rhodes
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August 15, 2023
Path Sum: Three Ways
NOTE: This problem is a more challenging version of Problem 81. The minimal path sum in the $5$ by $5$ matrix below, by starting in any cell...
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John Rhodes
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August 15, 2023
Path Sum: Two Ways
In the $5$ by $5$ matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down,...
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John Rhodes
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August 15, 2023
Square Root Digital Expansion
It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square...
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John Rhodes
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August 15, 2023
Coin Partitions
Let $p(n)$ represent the number of different ways in which $n$ coins can be separated into piles. For example, five coins can be separated into piles in...
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John Rhodes
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August 15, 2023
Prime Summations
It is possible to write ten as the sum of primes in exactly five different ways: \begin{align} &7 + 3\\ &5 + 5\\ &5 + 3 +...
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John Rhodes
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August 15, 2023
Counting Summations
It is possible to write five as a sum in exactly six different ways: \begin{align} &4 + 1\\ &3 + 2\\ &3 + 1 + 1\\ &2...