0 votes 0 votes How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and ($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5? My answer comes to be 26. Please confirm. Combinatory pigeonhole-principle discrete-mathematics + – Ayush Upadhyaya asked Jun 23, 2018 Ayush Upadhyaya 459 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Shubhgupta commented Jun 23, 2018 reply Follow Share Yes answer will be 26 because a can have 5(0,1,2,3,4) values and b can have 5 values and 5*5 = 25 ordered pairs are possible with each distinct pair of class now by the rule of pigeonhole if we add 1 then there exist at least two pair which belong to the same class. so total no of ordered pairs = 25 +1 =26 0 votes 0 votes srestha commented Jun 23, 2018 reply Follow Share https://gateoverflow.in/219084/number-of-ordered-pairs 0 votes 0 votes Deepak Poonia commented Jun 24, 2018 reply Follow Share Yes. Answer is 26. Refer the link srestha ma'am shared if any doubt. 0 votes 0 votes Please log in or register to add a comment.