Misprints and Rarities
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#230:Sum Other Way
Consider the following equations:
1 = 0 + 12 + 34 + 5 - 67 +8 +9
2 = 0 + 123 + 4 - 56 - 78 + 9
3 = 0 + 123 -45 -6 -78 + 9
4 = 0 + 12 +3 - 4 + 5 - 6 - 7 - 8 + 9
The numbers on the left side of the equations are calculated by using each of the digits 0 through 9, in any order, exactly once and either concatenating those digits or seperating them with a plus (+) or minus (-) sign.
What is the smallest positive number for which you cannot write such an equation?
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Notes found among the papers of Neville Ashberyy, antiquary. c. 70-80 AC
In a sale of books, purchased three excellent volumes of Varkin, barely foxed, as well as two maps of the City dating from before the cataclysm and a bound copy of the census taken in 15AC, each inscribed with the name Thalian Reese. The last particularly intrigued me, for I have seen very few copies of this document and perhaps none in such fine condition. Upon opening the book, at home, I found some papers held between the pages of the census and, reading them, discovered the pitiable story I have copied our here. At first, I wondered if it might be a mere fiction but a day's enquiry at the Academy library confirmed that Reese did indeed experience the loss here documented, that he was, in fact, eventually forced to resign his post, so broken by grief was he.
The name William Oxbow interested me. From his notes in the margins of the census, Reese appears to have tracked down and spoken to anyone with the words Ox or Bow in their name, but with no success. I, however, remembered that it is an old family name of Peterfitch - rather remote in those times and all the more so after the cataclysm. I have written to several members of that family, enquiring as to whether there is a William among them, aged about 80 years. I have not much hope of receiving a positive response, but am sufficiently intrigued as to wish to continue the hunt.
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