Arrange numbers 2 to 20 to the hexagons, with rules :
- The difference between 2 connected hexagons (side by side) is more than 4
- Numbers inside the yellow hexagons are prime numbers.
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The answer is
First row: 2
Second row: 14 12
Third row: 4 7 6
Fourth row: 19 18
Fifth row: 9 13 11
Sixth row: 3 5
Seventh row: 17 20 16
Eighth row: 8 10
Ninth row: 15
- You start by noting that the three primes that border 9 must be 3, 17, 19. The location of 3 is then set since it must take the spot that borders 20.
- Next, note that 5 must be in one of the two yellow hexagons that are furthest to the right, or else it would border 2 or 3. The 7 must then be directly below the 2, or else it would border either 3 or 5.
- After that, note that the 11 must also be in one of the furthest two yellow hexagons, or else it would border 7 or 9. This fixes 13 as the one right below 7.
- From there, you can deduce that 5 is to the right of 13, and 11 is the prime furthest right (since the other way would have 11 border 13).
- And finishing off the primes, due to 13's location, the prime between 9 and 7 must be 19, and the last yellow hexagon is where 17 is located.
- Note that because 5,7,11,13 are all adjacent to a square and we already know the location of both 19 and 20, this square contains 18.
- From here, note that the only possible number above 18 left is 12, and the only possible number above 19 is 14.
- Next, note that the only number left that can be above 9 is 4.
- Next, note that the only number left that can border 11,12,18 is 6.
- 16 must then be below 11, since otherwise it would border 20.
- 15 must be below 20 or else it borders 16 or 17.
- 8 must then be below 3 (or else it would border 5), and 10 takes the remaining spot.