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Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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The sum of the three sides is either even, or odd. Even: e + e + e e + o + o Odd: o + o + o o + e + e Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e e + o + o Odd: o + o + o o + e + e Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e e + o + o Odd: o + o + o o + e + e = 2+4+6 = 12 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e= 2+4+6 = 12 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e= 2+4+6 = 12 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e= 2+4+6 = 12 e + e = o + o 2 4 6 1 5 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e= 2+4+6 = 12 e + e = o + o 4 2 6 3 5 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e= 2+4+6 = 12 e + e = o + o 2 4 6 1 3 5 Not possible! 2 must be placed in the middle. Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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6 2 4 Even: e + e + e= 2+4+6 = 12 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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6 2 4 3 1 5 Even: e + e + e= 2+4+6 = 12 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e e + o + o Odd: o + o + o o + e + e = 2+4+6 = 12 = 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + e = o + o Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + e = o + o 6 21 5 3 Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + e = o + o 3 4 2 5 1 Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + e = o + o 5 1 3 Not possible! 5 must be placed in the middle! Odd: o + o + o= 1+3+5 = 9 6 4 2 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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1 5 3 Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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1 4 65 23 Odd: o + o + o= 1+3+5 = 9 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e e + o + o Odd: o + o + o o + e + e = 2+4+6 = 12 = 1+3+5 = 9 odd at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + o = e + o 1 3 5 4 6 Even: e + o + oodd at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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1 53 Even: e + o + oodd at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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1 2 46 53 Even: e + o + oodd at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Even: e + e + e e + o + o Odd: o + o + o o + e + e = 2+4+6 = 12 = 1+3+5 = 9 odd at vertex even at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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e + o = o + e 2 4 6 3 5 Odd: o + e + eeven at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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2 35 64 Odd: o + e + eeven at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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2 1 35 64 Odd: o + e + eeven at vertex Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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6 3 21 45 1 4 65 23 1 2 46 53 2 1 35 64 Fill in the numbers 1-6 in each circle so that the sum of the three numbers on each side are equal.

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Choosing numbers randomly does not quickly lead to an answer. Solving the problem requires reasoning and simple computations. Prerequisites: Addition & Subtraction; Understanding of even and odd numbers. The problem is cracked when students deduce additional facts from the limited information provided.

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Slide R - 1 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall Active Learning Lecture Slides For use with Classroom Response.

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