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Omni-MATH / ( Elgin Johnston ) Legs L₁,L₂,L₃,L₄ of a square table each have length n , where n is a positive integer. For how many ordered 4-tuples (k₁,k₂,k₃,k₄) of nonnegative integers can we…

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problem

( Elgin Johnston ) Legs L1,L2,L3,L4L_1, L_2, L_3, L_4 of a square table each have length nn , where nn is a positive integer. For how many ordered 4-tuples (k1,k2,k3,k4)(k_1, k_2, k_3, k_4) of nonnegative integers can we cut a piece of length kik_i from the end of leg Li(i=1,2,3,4)L_i \; (i = 1,2,3,4) and still have a stable table? (The table is stable if it can be placed so that all four of the leg ends touch the floor. Note that a cut leg of length 0 is permitted.)
Plain-text mathematical notation (without MathML)
( Elgin Johnston ) Legs L₁,L₂,L₃,L₄ of a square table each have  length n , where n is a positive integer.  For how many ordered  4-tuples (k₁,k₂,k₃,k₄) of nonnegative integers can we cut  a piece of length k_(i) from the end of leg L_(i) (i=1,2,3,4) and still have a stable table?
(The table is stable if it can be placed so that  all four of the leg ends touch the floor. Note that a cut leg of length 0 is permitted.)
Original LaTeX notation
( Elgin Johnston ) Legs $L_1, L_2, L_3, L_4$ of a square table each have  length $n$ , where $n$ is a positive integer.  For how many ordered  4-tuples $(k_1, k_2, k_3, k_4)$ of nonnegative integers can we cut  a piece of length $k_i$ from the end of leg $L_i \; (i = 1,2,3,4)$ and still have a stable table?
(The table is stable if it can be placed so that  all four of the leg ends touch the floor. Note that a cut leg of length 0 is permitted.)

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Source and history

task_id
4f67cf3d-6dac-5bdc-9ae1-d0066d4aec1a
task_key
test--4f67cf3d-6dac-5bdc-9ae1-d0066d4aec1a
task_revision_id
1
config / split
/ test

Official source

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