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A prime butterfly is a set of three distinct numbers $a,b,c$, such that $a+b$ and $b+c$ are both primes. Can you divide numbers from 1 to 30 into 10 prime butterflies?

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First, observe the facts that:

Each triplet must be either an Even-Odd-Odd triplet, or an Odd-Even-Even triplet. Now there are 15 Odd and 15 Even numbers between 1 and 30. Hence, there will be 15 triplets of Even-Odd-Odd combination, and another 15 of Odd-Even-Even combination. After this, I started putting the first 5 even numbers (one in each triplet) to populate the first 5 triplets.

Proceeding further, the final answer is then:

enter image description here

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  • $\begingroup$ Maybe fix the headings in the right hand table to "odd even even" $\endgroup$ – theonetruepath Nov 7 '19 at 23:58
  • $\begingroup$ Sorry..changed now $\endgroup$ – SamRoy Nov 8 '19 at 0:02
  • $\begingroup$ Correct! Well done. $\endgroup$ – Dmitry Kamenetsky Nov 8 '19 at 0:52

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