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 Skip Navigation LinksMath Help > Math Puzzles > 2004 State Logic Quiz > Question 07 > Question 07

Academic Decathlon 2004 State Championship Logic Quiz

Question 07

Place the numbers 0, 6, 12, 18, 24, and 30 in the six squares so that the sum of the four numbers on each circle is 60:

Answer:

There are a few ways to do this.  One is

Here's a good way to approach this problem.  Pick a circle, and look at the four squares on that circle.  Now look at the triangular pattern formed by the six squares, and see which two the circle does not go through.  You should see that a given circle goes through all the squares except one corner of the triangle and the middle of the opposite side.

For example, the circle that goes through 24, 12, 6, and 18 "misses" 30 and 0 -- 30 is on the corner of the triangular pattern, and 0 is in the center of the opposite side.  Since 0+6+12+18+24+30=90, then the two numbers missed by the circle have to add up to 30 so that the other four add up to 60.

The three corner-side pairs, then, have to be

0,30;
6,24; and
12,18.

It really doesn't matter how these are arranged on the diagram, as long as one of each pair goes on a corner of the triangular pattern, and the other goes in the opposite side.

 

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