Harry's competitive math team has been ranked the number one team for the past 40 days. His team competes in a math competition at least once per day and competes in no more than 60 competitions in these 40 days. Show that there is some day $i$ and some day $j$ such that between $i$ and $j$, exactly 19 matches have been played. \\ \\

Answer for the question:

Harry's competitive math team has been ranked the number one team for the past 40 days. His team competes in a math competition at least once per day and competes in no more than 60 competitions in these 40 days. Show that there is some day $i$ and some day $j$ such that between $i$ and $j$, exactly 19 matches have been played.

is given in the attachment.

Explanation:

answer///a road map;