Sunday Times Teaser 2895 – Spanish and Latin

by Graham Smithers

Published March 18 2018 (link)

I have ten cards. For each card there is a number in Spanish on one side and a number in Latin on the other.

The Spanish numbers are CINCO, CUATRO, DIEZ, DOS, NUEVE, OCHO, SEIS, SIETE, TRES and UNO. The Latin numbers are DECEM, DUO, NOVEM, OCTO, QUATTUOR, QUINQUE, SEPTEM, SEX, TRES and UNUS. For each of the ten pairs of numbers, there are two letters in common. If I told you on how many cards the two numbers were consecutive, you should be able to work out all ten pairings. The Spanish numbers are written alphabetically.

What is the corresponding order for the Latin numbers?

One Comment Leave one →

Brian Gladman permalink

This uses my solver for this type of grouping problem (grouping.py)


from collections import defaultdict
from grouping import groups, output_groups, shared_letters

# spanish words for numbers 1..10
sp = ('UNO', 'DOS', 'TRES', 'CUATRO', 'CINCO', 
      'SEIS', 'SIETE', 'OCHO', 'NUEVE', 'DIEZ')

# latin words for numbers 1..10
lt = ('UNUS', 'DUO', 'TRES', 'QUATTUOR','QUINQUE', 
      'SEX', 'SEPTEM', 'OCTO', 'NOVEM', 'DECEM')

# for saving solutions indexed on the consecutive number count
c2s = defaultdict(list)

# consider possible groupings where each pair of numbers share
# exactly two (possibly repeated) letters in common
for s in groups([sp, lt], shared_letters(2)):
  # count number pairings in which the paired numbers are consecutive
  cons = [abs(sp.index(ns) - lt.index(nl)) for ns, nl in s].count(1)
  c2s[cons].append(s)

# look for a consecutive number count that uniquely identifies a pairing
for c, (s, *r) in c2s.items():
  if not r:
    # output the latin number in each pair for the 
    # spanish numbers in alphabetical order
    print(', '.join(tuple(y for x, y in sorted(s))))

from collections import defaultdict

from grouping import groups, output_groups, shared_letters

# spanish words for numbers 1..10

sp = ('UNO', 'DOS', 'TRES', 'CUATRO', 'CINCO',

'SEIS', 'SIETE', 'OCHO', 'NUEVE', 'DIEZ')

# latin words for numbers 1..10

lt = ('UNUS', 'DUO', 'TRES', 'QUATTUOR','QUINQUE',

'SEX', 'SEPTEM', 'OCTO', 'NOVEM', 'DECEM')

# for saving solutions indexed on the consecutive number count

c2s = defaultdict(list)

# consider possible groupings where each pair of numbers share

# exactly two (possibly repeated) letters in common

for s in groups([sp, lt], shared_letters(2)):

# count number pairings in which the paired numbers are consecutive

cons = [abs(sp.index(ns) - lt.index(nl)) for ns, nl in s].count(1)

c2s[cons].append(s)

# look for a consecutive number count that uniquely identifies a pairing

for c, (s, *r) in c2s.items():

if not r:

# output the latin number in each pair for the

# spanish numbers in alphabetical order

print(', '.join(tuple(y for x, y in sorted(s))))

Sunday Times Teaser 2895 – Spanish and Latin

by Graham Smithers

Published March 18 2018 (link)

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