Sunday Times Teaser 2700 – Spell Check
by Victor Bryant
When the number 2700 is expressed both in words and as a product of its prime factors:
TWO THOUSAND SEVEN HUNDRED = 2 2 3 3 3 5 5
it can be seen that the number of letters is equal to the sum of its factors.
This is also true for an odd numbered teaser published in the last decade.
What is the number of this teaser?
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brian gladman permalink123456789101112131415161718192021222324252627282930313233343536373839from number_theory import factors# convert number to word form for numbers less than 10 ** 36l_lo = ( '', 'one', 'two', 'three', 'four', 'five', 'six', 'seven','eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen','fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen','nineteen' )l_10 = ( 'twenty', 'thirty', 'forty', 'fifty', 'sixty', 'seventy','eighty', 'ninety')l_hi = ( ' thousand', ' m', ' b', ' tr', ' quadr', ' quint',' sext', ' sept', ' oct', ' non', ' dec' )def int_as_words(x, commas=True, l=0):if x >= 10 ** 36:raise NotImplementedErrorif x < 0:return 'minus ' + int_to_words(-x)if x < 20:return l_lo[x] if x else 'zero'elif x < 100:return (l_10[x // 10 - 2] + ('', ' ')[x % 10 > 0] + l_lo[x % 10])elif x < 1000:return (l_lo[x // 100] + ' hundred' +('', ' and ' + int_as_words(x % 100, l))[x % 100 > 0])else:t = int_as_words(x // 1000, commas, l + 1)u = ('', l_hi[l] + ('', 'illion')[l > 0])[(x // 1000) % 1000 > 0]v = ('', ',')[commas] + (' ', ' and ')[l == 0 and x % 1000 < 100]v = ('', v + int_as_words(x % 1000, commas, l))[x % 1000 > 0]return t + u + vfor nbr in range(2201, 2702, 2):wds = int_as_words(nbr, commas=False)f = tuple(factors(nbr))wd = wds.replace(' ', '')if len(wd) == sum(f):print('Teaser Number {} ({} = {})'.format(nbr, wds, f))
