Recently I've been using Twitter to create a daily tweet that records my "day count" (number of days I've been alive) plus its factors (if not prime) and some interesting facts about the number itself or one of its factors. Sometimes there's little to say about the number and in such cases I've found that I can usually form an equation by inserting mathematical operators between one or more of the digits.
For example, yesterday the count was 23518 and 23-5=18. Today the count is 23519 and 2+3+5-1=9. I was wondering if it's always possible to create an equation from five digits using the standard mathematical operators (addition, subtraction, multiplication, division and exponentiation in combination with brackets). Obviously with just two digits, it's only possible when the digits are repeated e.g. 99 becomes 9=9. With three digits, it's sometimes possible e.g. 819 becomes 8+1=9 but generally it isn't e.g. 219. With four digits, it's more possible e.g. 2119 becomes -2+11=9 but I'm doubtful whether this is always so. There must come a point however, where the number of digits is sufficient to ensure that it's always so. Maybe five digits is that point.
From now on, I'll try each day to form an equation to test out this theory. For example, tomorrow the count is 23520 which becomes 2+3-5=2x0 and it works for tomorrow but beyond that let's see.
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