Sunday Times Teaser 2979 – Mischievous Sam

1. 
   Brian Gladman permalink

   Python

   from collections import defaultdict # return the digits of a decimal number (n) in base (b) def in_base(n, b): dgts = [] while n: n, r = divmod(n, b) dgts.append(r) return dgts[::-1] # map wrong digit positions to the (answer, base) p2s = defaultdict(list) # the last digit of the number for ld in range(3, 10): # the number and its digits in decimal nbr = 111 * ld - 210 dgts = [ld - 2, ld - 1, ld] # consider bases that can give less than four digits for base in range(4, 10): bdgts = in_base(nbr, base) if len(bdgts) == 3: # look for different digits in decimal and base representations # and collect their positions pos, *r = [i for i, (x, y) in enumerate(zip(dgts, bdgts)) if x != y] # if only one digit is different, store the (answer, base) result # indexed on its position if not r: p2s[pos].append((nbr, base, ''.join(str(x) for x in bdgts))) # look for a position that gives a unique (answer, base) pair for (nbr, base, dgts), *r in p2s.values(): if not r: print(f"{nbr} (base 10) -> {dgts} (base {base})")

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   from collections import defaultdict   # return the digits of a decimal number (n) in base (b) def in_base(n, b):   dgts = []   while n:     n, r = divmod(n, b)     dgts.append(r)   return dgts[::-1]   # map wrong digit positions to the (answer, base) p2s = defaultdict(list)   # the last digit of the number for ld in range(3, 10):   # the number and its digits in decimal   nbr = 111 * ld - 210   dgts = [ld - 2, ld - 1, ld]   # consider bases that can give less than four digits   for base in range(4, 10):     bdgts = in_base(nbr, base)     if len(bdgts) == 3:       # look for different digits in decimal and base representations       # and collect their positions       pos, *r = [i for i, (x, y) in enumerate(zip(dgts, bdgts)) if x != y]       # if only one digit is different, store the (answer, base) result       # indexed on its position       if not r:         p2s[pos].append((nbr, base, ''.join(str(x) for x in bdgts)))   # look for a position that gives a unique (answer, base) pair         for (nbr, base, dgts), *r in p2s.values():   if not r:     print(f"{nbr} (base 10) -> {dgts} (base {base})")

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