perplexus.info :: Numbers : Squares Probability

Squares Probability (Posted on 2003-06-19)

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"?

Submitted by Gamer

Rating: 3.7000 (10 votes)

Solution: (Hide)

If you look at a list of squares (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100) you will note there isn't any 2, 3, 7, or 8 in the ones place.

Since squaring any ones place number never will give 2, 3, 7 or 8 (because 0 thru 9 don't give it), you can't ever have a perfect square that ends with 2,3,7 or 8. This means the answer is 0.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-04 09:50:44
solution	CharleyA.	2007-01-24 16:06:45
Good Q	Dave Cheetham	2003-08-17 13:55:17
re: can't be. . .	Sanjay	2003-06-29 02:31:41
can't be. . .	becca	2003-06-28 23:31:35
Zero	Rajeev	2003-06-23 21:44:07
squares?	mark hartman	2003-06-19 18:13:59
re(4): Solution	Gamer	2003-06-19 15:35:49
re(3): Solution	Sanjay	2003-06-19 10:50:35
No entry for squares	Sanjay	2003-06-19 10:35:11
re(2): Solution	Hank	2003-06-19 05:40:59
re: Solution	Gamer	2003-06-19 05:35:13
Solution	Hank	2003-06-19 04:21:21

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