UPSC CDS 2 2021 Math Paper

Let five consecutive integers be in the form (x−2),(x−1),x,(x+1) and (x+2).
Since, it is given that the product of these five consecutive integers is equal to one of these integers. This is only possible when one of the integer is zero.
Hence, all possible sequences are
(i) −4,−3,−2,−1,0
(ii) −3,−2,−1,0,1
(iii) −2,−1,0,1,2
(iv) −1,0,1,2,3
and (v) 0,1,2,3,4
Hence, number of required sequences will be five.