Inserting Plus Signs and Adding. Issue 3 (1st March 2016)

• Record Type: Journal Article
• Authors: Butler, Steve; Graham, Ron; Stong, Richard
• Is Part Of: American Mathematical Monthly. Volume 123:Issue 3(2016)
• Page Start: 274
• Page End: 279
• Publication Date: 2016-03-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.123.3.274
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: For a fixed base b, we consider the following operation called "insert and add" on a natural number: Write the number as a string of digits and between some of the digits insert a plus sign; finally, carry out the indicated sum. If at least one plus sign is inserted, this results in a smaller natural number and so repeated application can always reduce the number to a single digit. We show that for any base b, surprisingly few applications of this operation are needed to get down to a single digit.