From a posting to the Math Fun mailing list by R. W. Gosper, Dec 03 2009:
Gosper: I just reordered checks.
Bank Lady: Where would you like the numbering to start?
Gosper: What was my last one?
Bank Lady: 1093
Gosper: Well then obviously 3511 .
Bank Lady: [Opens mouth. Decides not to ask. Resumes typing.]
My question : How many checks can you order for
Mr. Gosper's checkbook, using his numbering system?
I think the best answer is 4141.
If we assume the previous chequebook ended at 1093, i.e. 'What was my last one?' refers to the number of the last cheque in the previous chequebook, then the problem is open-ended, for any number of reasons.
So it is reasonable to assume that Gosper's enquiry 'What was my last one?' is an ellipsis for 'Where did the numbering start last time?' in which case the puzzle is readily answered.
Assuming the previous chequebook started at 1093, it would for reasons too obvious to mention have contained the 2187 cheques ending with 3279.
Similarly the new chequebook would contain cheques numbered from 3511 to 7651 inclusive - a total of 4141 cheques.
I should add though that in practice it would be unusual for the bank to accept an order, particularly from an agent, for more than 50-100 cheques at a time, for security reasons.
Edited on September 20, 2012, 11:00 am
Posted by broll
on 2012-09-20 10:42:10