N-propositions-are-judged-by-2k-1-people-Each-person-assigns-true-to-exactly-M-propositions-and-false-to-the-other-N-M-M-N-To-say-a-proposition-is-approved-means-it-is-true-according-to-at

Question Number 18361 by diofanto last updated on 19/Jul/17

N propositions are judged by 2 k - 1 people .

Each person assigns “ {true}^{″} to

exactly M propositions and “ {false}^{″}

to the other N - M (M ⩽ N) .

To say a proposition is “ {approved}^{″} means

it is true according to at least k judges .

Find the minimum and maximum numbers

of approved propositions given N, M and k .