Sunday Times Teaser 3078 – Digital DaisyChains
by Victor Bryant
Published Sunday September 19 2021 (link)
The number 798 is a “digital daisychain”; ie, if you spell out each of its digits as a word, then the last letter of each digit is the first letter of the next. Furthermore, the number 182 is a “looped” digital daisychain because, in addition, the last letter of its last digit is the first letter of its first digit.
I have written down a large looped digital daisychain (with fewer than a thousand digits!). The total of its digits is itself a digital daisychain.
What is that total?
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Erling Torkildsen permalink123456789101112131415161718192021222324# Valid links in a 'daisychain'OK = {"01", "18", "21", "38", "58", "79", "82", "83", "98"}def is_daisy(n):s, l, j = str(n), len(str(n)), set()for i in range(l  1):j.add(s[i] + s[i + 1] in OK)return all(j)# Structure 'looped daisychains' are head + body + tail## body = (8 + 3)*n or (8 + 2 + 1)*n ie allways 11*n## 1 + 11*n + 8 + 2 # 2 + 1 + 11*n + 8 # 3 + 11*n + 8 > 11*(n + 1)# 11*n + 8 + 3 #for n in range(501):if is_daisy(11*(n + 1)):print("Total:", 11*(n + 1))