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Omni-MATH / Kelvin the Frog has a pair of standard fair 8-sided dice (each labelled from 1…

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problem

Kelvin the Frog has a pair of standard fair 8-sided dice (each labelled from 1 to 8). Alex the sketchy Kat also has a pair of fair 8-sided dice, but whose faces are labelled differently (the integers on each Alex's dice need not be distinct). To Alex's dismay, when both Kelvin and Alex roll their dice, the probability that they get any given sum is equal! Suppose that Alex's two dice have aa and bb total dots on them, respectively. Assuming that a≠ba \neq b, find all possible values of min{a,b}\min \{a, b\}.
Plain-text mathematical notation (without MathML)
Kelvin the Frog has a pair of standard fair 8-sided dice (each labelled from 1 to 8). Alex the sketchy Kat also has a pair of fair 8-sided dice, but whose faces are labelled differently (the integers on each Alex's dice need not be distinct). To Alex's dismay, when both Kelvin and Alex roll their dice, the probability that they get any given sum is equal! Suppose that Alex's two dice have a and b total dots on them, respectively. Assuming that a≠b, find all possible values of min{a,b}.
Original LaTeX notation
Kelvin the Frog has a pair of standard fair 8-sided dice (each labelled from 1 to 8). Alex the sketchy Kat also has a pair of fair 8-sided dice, but whose faces are labelled differently (the integers on each Alex's dice need not be distinct). To Alex's dismay, when both Kelvin and Alex roll their dice, the probability that they get any given sum is equal! Suppose that Alex's two dice have $a$ and $b$ total dots on them, respectively. Assuming that $a \neq b$, find all possible values of $\min \{a, b\}$.

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Source and history

task_id
016ee311-57b0-5d18-ba8c-3e1df4e25e70
task_key
test--016ee311-57b0-5d18-ba8c-3e1df4e25e70
task_revision_id
1
config / split
/ test

Official source

initial import