Related To Magic Square?

Number Theory Level 2

How many ways can we obtain a sum of 15 by adding up 3 distinct digits from 1 to 9?

6 8 10 15

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Ossama Ismail
Feb 4, 2017

The 3 x 3 magic square :

| 8 | 1 | 6 |

| 3 | 5 | 7 |

| 4 | 9 | 2 |

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Yes, all of those equations are represented in the magic square. How do we know that there aren't more?

For example, it is no longer true that there are only 10 ways to find 4 distinct integers from 1 to 16 that sum to 34.

Calvin Lin Staff - 4 years, 4 months ago

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Thinking about magic squares led me to this problem. I was surprised that there were only those equations. Is it just coincidence, or is there some deeper meaning?

Chung Kevin - 4 years, 4 months ago

1+5+9=15

1+6+8=15

2+4+9=15

2+5+8=15

2+6+7=15

3+4+8=15

3+5+7=15

4+5+6=15

answer: 8 \boxed{8}

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So the answer is at least 8. How do we know there aren't more?

Nick Schreiner - 4 years, 4 months ago

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This is related to the magical square, where the sum of all three numbers is 15 15 .

Michael Huang - 4 years, 4 months ago

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