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...
-
John Rhodes
-
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...
-
John Rhodes
-
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...
-
John Rhodes
-
August 15, 2023
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...
-
John Rhodes
-
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...
-
John Rhodes
-
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...
-
John Rhodes
-
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,...
-
John Rhodes
-
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...