Suppose you had number cards in a deck, such that you had 2 2s, 3 3s, 7 7s, and 8 8s. (and no other cards in that deck)

If you were to shuffle the deck (consider the cards to be random after shuffling) and take off the first 4 cards, (such that the first card is thousands place, the second card is the hundreds place, so on), what is the probability that this number will be a perfect square?? Also, how would you find this probability without "trial and error" or "brute force"?

(In reply to re(2): Solution by Hank)

Aren't we forgetting the zero?

Possible digits in the ones column of any number are 0-9. Therefore, the digit in the ones column of any perfect square will be the last digit in the squares of 0-9.

0*0=0
1*1=1
2*2=4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49

These happen to be 0,1,4,5,6 and 9.

Posted by Sanjay on 2003-06-19 10:50:35