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Programming Enigma Puzzles

8 April 2013

Posted by on **From New Scientist #2604, 19th May 2007**

It pains me that the two fastest cricket match centuries (by Viv Richards in 1986 off 56 balls and by Adam Gilchrist in 2006 off 57 balls) have both been scored against my namesake team. I retaliated by scoring a century off even fewer balls against the bowling of Shane Warne and Glenn McGrath and thus forced them into retirement.

In reaching my century I faced balls off which I had scores of 0, 1, 2, 4 and 6 runs, a different perfect square number of balls for each of these scores.

Exactly how many runs had I scored in total after completing the runs from the ball that bought me to my century?

[enigma1443]

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The following Python program runs in 44ms.

Solution:The total number of runs when the century was achieved is 103.There are two different ways that the century could be achieved:

or

In each case the century is scored off 55 balls, and in each case the score off the ball that gives the century could be a 4, taking the score from 99 to 103, or a 6, taking the score from 97 to 103.