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Difficult Envelope Problem
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Posted 07 April 2009 - 07:48 PM
I have a similar but difficult problem that's got me baffled for a while now. Please help me if you can. Thanx
There are 6 sealed envelopes, whose sizes are listed here:
4.125" x 9.5" Business envelope
3.5" x 9.25" Chou 30 envelope (from Japan)
4" x 5.5" Greeting card envelope
9" x 12" Large manila envelope
7.5" x 10.5" Small manila envelope
9.125" x 9.125" Square envelope
Each envelope has a single digit written on the outside of it. Some of the envelopes are inside of others; there's even one envelope that's inside an envelope that's inside another one. All of the envelopes are lying flat; They haven't been folded, cut, rolled, wrinkled, or otherwise modified them to make them fit.
You'll need to figure out what number is written on each envelope, from the clues below:
Exactly four of the envelopes are inside of other envelopes. One of the two "outside" envelopes has a transparent window, through which the number 7 is visible. Except for that window, the envelopes are opaque.
The number on the greeting card envelope equals the number on one of the other envelopes; there are no other duplicate numbers.
The product of the 6 numbers is 20160.
The number on the square envelope equals the number of envelopes inside it.
The number on the Chou 30 envelope is the sum of two of the other numbers.
The number on the large manila envelope equals the average of the numbers on the envelopes inside it.
Posted 28 December 2009 - 07:17 PM
Wow, that's beastly.
A few hints..
It may help to make a table to eliminate possibilities.
First calculate the area of each and order them greatest to least. that way you know what fits in what.
We know the seven can't be on the largest envelope, because the seven envelope is inside something else.
Also we know the product of the non-seven numbers, which is 20161 divided by seven.
The result is the product of five numbers with only one digit. From that you may be able to get the numbers, then you just have to match them with the envelopes.
See if you can write at least a few of these as equations and work with them as a system of equations. You obviously can't graph, but use substitution, manipulation, and all that jazz and see if that helps.
Hope all this helps.
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