Praetorian wrote:

Code: md ( its for my reference, dont worry about it)

Level : Advanced (if you do it under time limits

)

1. Time yourself

2. Solve as fast as you can

3. Please write your solution, and your time please.

Three problems were given to participants of a math contest. Each participant got 0,1,2, or 3 points for each problem. After the papers were graded, it turned out that no pair of participants received matching scores for more than one problem. What is the largest possible number of participants?

a. 8

b. 9

c. 12

d. 16

e. 24

Answer should be 24:

Solution:

total results possible 4 * 4 * 4 = 64

(3 questions and for each question 4 grades possible)

Now apply limitation that

no pair of participants received matching scores for more than one problem,

__

000 |

001 | ---> Select only one pair from these, and remove other 3

002 |

003__|

__

010 |

020 | ---> Select only one from these, and remove other 2

030__|

__

100 |

200 | ---> Select only one from these, and remove other 2

300__|

Total remove = 3 + 2 + 2 = 7

If we do for each grade points, total removal = 7 * 4 = 28

So we are left with 64 - 28=36

out of 36, remove:

_

012 |--------> Remove any 1

013_|

_

021 |--------> Remove any 1

023_|

_

031 |--------> Remove any 1

032_|

Total removal will become 3 * 4=12 ( Pairs could be - 01, 02, 03, 10, 12, 13, 20, 21, 23, 30, 31, 32)

Remaining would be 36 - 12 = 24

If there is any flaw in solution, please let me know.

Dharmin