perplexus.info :: General : Six boxes

Six boxes (Posted on 2003-08-14)

There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue.

One sales man sold one box out of them and then he says, "I have the same number of red and blue balls left over."

Which box is sold out?

Submitted by Ravi Raja

Rating: 2.0000 (10 votes)

Solution: (Hide)

He sold the box with 29 balls.
The total number of balls: 5 + 7 + 14 + 16 + 18 + 29 = 89.

Total number of balls are odd. Also, there are the same number of red balls and blue balls are left out after selling one box. That can only happen if the remaining number of balls is even, so a box with odd number of balls in it must have been sold out (5, 7 or 29).

Now using trial and error:
(89-29) /2 = 60/2 = 30
and
14 + 16 = 5 + 7 + 18 = 30

More checking reveals that this does not work for the 5- or 7-ball boxes.

So the box with 29 balls was sold out, leaving 16+14=30 of one color and 5+7+18=30 of the other.

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

Subject	Author	Date
Explanation to Puzzle Answer	K Sengupta	2022-07-19 00:46:58
Puzzle Answer	K Sengupta	2022-03-26 23:59:54
Hmm, should I?	Lawrence	2003-08-24 06:39:18
No Subject	Dave Cheetham	2003-08-17 12:26:48
SOLUTION	lesa	2003-08-16 22:57:32
Solution	ethan	2003-08-15 12:56:40
Simple	DJ	2003-08-15 07:34:02
now my solution for THIS one	FatBoy	2003-08-14 18:49:13
oops	FatBoy	2003-08-14 18:47:58
2 Solutions (but one's a cheat)	FatBoy	2003-08-14 18:46:59
re: Solution	DuCk	2003-08-14 14:34:47
Solution	Bryan	2003-08-14 14:28:27

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