Of the first 2011 numbers, what is the minimum number that we have to draw randomly in order to ensure that there are: a) at least 2 numbers whose difference is exactly 111, and b) whose difference is 111 or greater? Thank you for help.
a) - 1 to 111 - keep
112 to 222 - skip
223 to 333 - keep
334 to 444 - skip
445 to 555 - keep
556 to 666 - skip
667 to 777 - keep
778 to 888 - skip
889 to 999 - keep
1000 to 1110 - skip
1111 to 1221 - keep
1222 to 1332 - skip
1333 to 1443 - keep
1444 to 1554 - skip
1555 to 1665 - keep
1666 to 1776 - skip
1777 to 1887 - keep
1888 to 1998 - skip
1999 to 2011 - keep [Remainder of the last 13]
Total ==[9 x 111] + 13 ==999 + 13 ==1012
Minimum number==1012 + 1==1013.
b) - Any 111 + 1 ==112 numbers drawn, there will always be a difference of at least 111 between the largest and the smallest numbers drawn.
