MathDB

Initially given

31

tuplets

(1,0,0,\dots,0),(0,1,0,\dots,0),\dots, (0,0,0,\dots,1)

were written on the blackboard. At every move we choose two written

31

tuplets as

(a_1,a_2,a_3,\dots, a_{31})

and

(b_1,b_2,b_3,\dots,b_{31})

, then write the

31

tuplet

(a_1+b_1,a_2+b_2,a_3+b_3,\dots, a_{31}+b_{31})

to the blackboard too. Find the least possible value of the moves such that one can write the

31

tuplets

(0,1,1,\dots,1),(1,0,1,\dots,1),\dots, (1,1,1,\dots,0)

to the blackboard by using those moves.

4