perplexus.info :: Just Math : Products of 22

Products of 22 (Posted on 2002-12-23)

The sum of the elements of a set of positive integers is 22.
What is the greatest possible product of the integers in this set if:

A Duplicates are allowed?
B Duplicates are not allowed?

Problem modified from UNL Math Day with help from friedlinguini

Submitted by cges

Rating: 3.2222 (9 votes)

Solution: (Hide)

If duplicates are allowed, you should choose the integers to be as close to e as possible.
That is, use six 3’s and one 2.
The answer is 2916.
If duplicates are not allowed, the maximum product is still generally found when all the numbers are as close as possible to e.
Inspection shows that 2, 3, 4, 6, 7 is better than 1, 2, 3, 4, 5, 7, so the maximum product is 2*3*4*6*7=1008.

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

Subject	Author	Date
Answer	Praneeth	2007-08-17 08:46:08
Puzzle solution with explanation	K Sengupta	2007-05-16 06:10:45
answer	K Sengupta	2007-05-16 06:00:04
re(2): Solution by ananth	Jer	2004-05-03 12:10:11
re: Solution by ananth	Jer	2003-03-28 08:08:11
Solution	ananth	2002-12-26 00:46:00
solution	Cory Taylor	2002-12-24 04:00:55

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