Sally, Joe, Bob, Fred, and Mary all won a prize in the school lottery. One of them won $500; one of them $196; another won $48; another, $16; and another, $2. Each of the students won in a different month: February, March, September, October, and December. How much money did each student win and in what month?

Clues:

1. At least one of the winners' names begins with the same letter as his or her winning month.

2. The girls won a total less than $250 and more than $205

3. One of the people with the shortest names won the least and the other won the most.

4. Mary won the month before Joe.

5. One of the girls won just in time for Christmas shopping.

6. The March and September winners won the most.

7. Sally won more than Fred

You are abolutely correct Rachael (solutions at the end)

Pt 1.From clue 3 its evident that bob and joe win $500 and $2 (ofcourse we can't say "respectively")

Pt 2.Mary and Sally (the two girls) must have won either ($196 and $48) or ($196 and $16) .....see clue 2

Pt 3.Now see clues 4 and 5 , it seems from clue 5 that one of the gals won in december but Mary won a month before joe so she cudn't have won in december (the last month) . So Sally won in december .  

Pt 4. One interesting things from Pt 1 and Pt 2 it seems Fred won either $48 if gals won ( $196 and $16 ) or $16 if gals won ($196 and $48)

Pt 5. March and september have the highest winners .... who win $196 and $500(won by Bob or Joe) ..... now as Sally wins in December(Pt 3) and $196 is won by a gal(Pt 2) in september or march ....surely Sally is not the girl , so Mary wins $196 in either march or september

Pt 6. But Mary won a month before Joe ...didnt she .....  so she must have won in september coz we have a winner in october (the following month of september ) but not in april (the following month of  march)

Pt 7. Let us again see if Mary wins in September and Joe follows in October (from above) ....from Clue 6 we can see that Joe is not the highest winner so from Pt 1 we conclude that Joe wins $2 in october that is, he is the lowest winner. 

Pt 8. So Bob must have won $500 in month March Pt 5,6,7 (simply read them ,no rocket science) 

Pt 9. Now Sally and Fred won $48 and $16 (respectively this time because Sally wins more than Fred Clue 7 ) and obviously Fred wins in the only month left ,that is, Feburary

     Bob   $500     March

     Mary $196     September

     Sally $48       December

     Fred $16        Feburary

     Joe   $2          October

 

The catch : Observe the clues used (i highlighted them on  purpose ) ..... we did'nt need Clue 1 now if u say Clue 1 is a condition not a clue than ok Pt 9 satisfies the condition sir Fred wins in Feb ..... but i still think it was a clue

Note : Pt 4 is only interesting it is not used !!!!!

Posted by phi on 2005-06-20 13:57:25