Sunday Times Teaser 2550 – Cricket Averages

by Graham Smithers

Published: 7 August 2011 (link)

Playing for our local team, Sam and Oliver between them took 5 wickets in each innings, taking 5 wickets each overall. Sam’s averages (ie runs per wicket) were lower than Oliver’s in both innings, but overall Sam had the higher average. All six averages were single non-zero digits.

If you knew Sam’s overall average, it would then be possible to calculate the number of runs scored against Sam and against Oliver.

What were the total runs scored against a) Sam and b) Oliver?

One Comment Leave one →

Brian Gladman permalink


from itertools import product
from collections import defaultdict

d = defaultdict(set)
# Sam's wickets taken in the first innings
for s1 in range(1, 5):
  
  # Oliver's wickets taken in the first innings and
  # Sam and Oliver's taken in the second innings 
  o1, s2, o2 = 5 - s1, 5 - s1, s1

  # try Sam's single digit averages in the two innings
  for sav1, sav2 in product(range(1, 10), repeat=2):

    # calculate Sam's overall average which must be
    # a whole number
    sav3, rem = divmod(sav1 * s1 + sav2 * s2, 5)
    if not rem:
      
      # now try Oliver's averages in the two innings
      # which are higher than Oliver's
      for oav1, oav2 in product(range(sav1 + 1, 10), range(sav2 + 1, 10)):
        
        # calculate Oliver's overall average which must be
        # a whole number less than Sam's 
        oav3, rem = divmod(oav1 * o1 + oav2 * o2, 5)
        if not rem and oav3 < sav3:
          
          # now save the overall runs scored against Sam
          # and Oliver associated with Sam's average
          d[sav3].add((5 * sav3, 5 * oav3))

# now look for an Overall average for Sam that  leads to a
# unique answer for the runs scored against Sam and Oliver
for av in d.keys():
  score, *r = d[av]
  if not r:
    fs = ('The runs scored against Sam and Oliver are {} and {}'
          ' respectively.')
    print(fs.format(*score))

from itertools import product

from collections import defaultdict

d = defaultdict(set)

# Sam's wickets taken in the first innings

for s1 in range(1, 5):

# Oliver's wickets taken in the first innings and

# Sam and Oliver's taken in the second innings

o1, s2, o2 = 5 - s1, 5 - s1, s1

# try Sam's single digit averages in the two innings

for sav1, sav2 in product(range(1, 10), repeat=2):

# calculate Sam's overall average which must be

# a whole number

sav3, rem = divmod(sav1 * s1 + sav2 * s2, 5)

if not rem:

# now try Oliver's averages in the two innings

# which are higher than Oliver's

for oav1, oav2 in product(range(sav1 + 1, 10), range(sav2 + 1, 10)):

# calculate Oliver's overall average which must be

# a whole number less than Sam's

oav3, rem = divmod(oav1 * o1 + oav2 * o2, 5)

if not rem and oav3 < sav3:

# now save the overall runs scored against Sam

# and Oliver associated with Sam's average

d[sav3].add((5 * sav3, 5 * oav3))

# now look for an Overall average for Sam that leads to a

# unique answer for the runs scored against Sam and Oliver

for av in d.keys():

score, *r = d[av]

if not r:

fs = ('The runs scored against Sam and Oliver are {} and {}'

' respectively.')

print(fs.format(*score))

Sunday Times Teaser 2550 – Cricket Averages

by Graham Smithers

Published: 7 August 2011 (link)

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