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 Math Help > Math Puzzles > 2004 Logic Quiz > Do They Add Up? > Do They Add Up?

# Academic Decathlon 2004 Logic Quiz

## Do They Add Up?  (300 points)

Insert the numbers 1 to 6 into the circles so that for any particular circle the sum of the numbers in the circles connected directly to it equals the value corresponding to the number, as given in the list.

 Example: 1 —> 14 (4+7+3) 3 —> 1 4 —> 8 (7+1) 7 —> 5 (4+1)

 1 —> 12 2 —> 9 3 —> 1 4 —> 14 5 —> 7 6 —> 4

There are two circles, marked "x" and "y", that lie on the "outskirts" of the graph -- i.e. each is connected to just one other circle, marked "a" and "b" on the diagram, below.  Circles "x" and "y" must point to the smallest sums (because all other circles are connected to other circles in addition to "a" or "b").

So these circle must be filled in as either

 or

In either case, there are just two ways to fill in the remaining two circles with the numbers 2 and 5.  So there are four combinations to try, altogether.  Process of elimination yields the answer:

 1 —> 12 2 —> 9 3 —> 1 4 —> 14 5 —> 7 6 —> 4

### Related pages in this website

See the NEXT puzzle in the Academic Decathlon 2004 Logic Quiz

The webmaster and author of this Math Help site is Graeme McRae.