|
Question 28573: Here's a little conundrum based on St. Peter's game. Say I have 11 cans, 5 of which contain tuna and 6 of which contain dog food. If I count off by nines, dropping every ninth can, am I guaranteed to end up with a can of tuna in the end. There is an easy way to prove this. First put them in alternating order and count off. Note there are also two ways of counting - either always starting(counting 1) with a can on one of the ends or starting (counting 1) with every tenth can.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Here's a little conundrum based on St. Peter's game. Say I have 11 cans, 5 of which contain tuna and 6 of which contain dog food. If I count off by nines, dropping every ninth can, am I guaranteed to end up with a can of tuna in the end.
YOU DID NOT MENTION ABOUT THE ORIGINAL ARRANGEMENT OF CANS.IT DEPENDS ON THAT.WE CAN ALWAYS ARRANGE TO GET A TUNA CAN OR DOG FOOD CAN TO BE THE LAST ONE TO BE PICKED UP.IF YOU WANT TO SEE HOW IT CAN BE DONE SEE THE FOLLOWING ON METHOD OF ARRANGEMENT FOR A SIMPLE CASE OF 2 TUNAS AND 3 OF DOG FOOD DROPPING EVERY ALTERNATE CAN ..YOU CAN EXTEND THE METHOD TO COVER ANY NUMBER/TYPE OF CANS CHOOSING ANY ONE NUMBER OR DIFFERENT NUMBERS TO DROP SUCCEEDING CANSAND TO SHOW THEM UP IN ANY ORDER YOU LIKE AT ANY POSITION...BEGINING..OR MIDDLE..OR END ..OR WHEREVER YOU LIKE...
........ON THE OTHER HAND IF THE CANS ARE PLACED AT RANDOM ONE CAN NEVER GUARANTEE..WE CAN ONLY TELL PROABILITY OF SUCCESS..BY ITS VERY NAME PROBABILITY IMPLIES THAT EVEN IF THE CHANCE IS ONE IN A MILLION ,STILL IT CAN HAPPEN OR NOT HAPPEN!!!!IN ANY CASE THIS WILL BE COMPLEX EXERCISE.
EXAMPLE ...2 TUNA CANS ...SAY T1,T2..
AND 3 DOGFOOD CANS SAY D1,D2,D3.
SAY WE COUNT IN TWOS OR DROP EVERY ALTERNATE ONE..TO GET D3 IN THE END ...NOT ONLY THAT..THEY SHOUD COME UP IN THE ORDER T1,T2,D1,D2 AND D3!!!PLACE THEM AS FOLLOWS
FOR PRACTICAL WORK TAKE ACE,TWO,THREE,FOUR AND FIVE FROM A PACK OF CARDS AND PLACE THEM ONE BELOW THE OTHER.FOR COUNTING/DROPPING,COUNT 1 SAY MOVE THE TOP CARD TO BOTTOM OF THE SET OF 5 AND DROP THE SECOND CARD.THEN AGAIN GO ON REPEATING THE PROCESS....
I...ARRANGE THEM IN ANY ORDER YOU LIKE SAY..
T1,T2,D1,D2,D3....NOW START COUNTING IN THE REQUIRED WAY AND REPLACE THE CARD COMING UP WITH THE ONE DESIRED..
COUNT ONE ...T1 GOES TO BOTTOM OF PACK .T2 IS OPENED OUT.BUT IT SHOULD BE T1..SO NOW CHANGE ORDER SO THAT THE REQUIRED CARD COMES IN THIS POSITION AND THE MOVED CARD TAKES ITS PLACE.SO NOW THE ORDER IS
II..T2,T1,D1,D2,D3 ..REPEAT THE PROCESS IN THIS WAY TILL YOU GET THE REQUIRED ORDER.
THE ANSWER IS
D1,T1,D3,T2,D2...
YOU CAN EVEN SPELL THEM ...SAY T U N A O N E AND SEE THAT THE SPELLED ONE COMES OUT AT THE END OF SPELLING THAT IS T1 COMES OUT ETC...
|
|
|
| |
