Stone Game
A game is played with three piles of stones and two players. On each player’s turn, the player may remove one or more stones from the piles....
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John Rhodes
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August 15, 2023
Reachable Numbers
A positive integer will be called reachable if it can result from an arithmetic expression obeying the following rules: Uses the digits $1$ through $9$, in that...
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John Rhodes
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August 15, 2023
A Lagged Fibonacci Sequence
A sequence is defined as: $g_k = 1$, for $0 \le k \le 1999$ $g_k = g_{k-2000} + g_{k – 1999}$, for $k \ge 2000$. Find $g_k...
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John Rhodes
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August 15, 2023
Tatami-Free Rooms
Tatami are rectangular mats, used to completely cover the floor of a room, without overlap. Assuming that the only type of available tatami has dimensions $1 \times...
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John Rhodes
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August 15, 2023
Rounded Square Roots
We define the rounded-square-root of a positive integer $n$ as the square root of $n$ rounded to the nearest integer. The following procedure (essentially Heron’s method adapted...
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John Rhodes
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August 15, 2023
Sums of Digit Factorials
Define $f(n)$ as the sum of the factorials of the digits of $n$. For example, $f(342) = 3! + 4! + 2! = 32$. Define $sf(n)$ as...
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John Rhodes
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August 15, 2023
Tidying Up A
A small child has a “number caterpillar” consisting of forty jigsaw pieces, each with one number on it, which, when connected together in a line, reveal the...
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John Rhodes
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August 15, 2023
Convex Holes
Given a set of points on a plane, we define a convex hole to be a convex polygon having as vertices any of the given points and...