10. Hexagram
Write the numbers from 1 to 12 in such a way that the sum of each straigh
row of 4 circles is 26.
Answers
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.In a magic square, 1 and the maximum number are usually paired. But in this puzzle, unlike a magic square, every number is included in exactly two sums. This gives us freedom we wouldn't normally have. We can pair 1 with 12 on the outside, but because of this freedom, we can put the next-most-extreme numbers together, to give us a place to start from:
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.In a magic square, 1 and the maximum number are usually paired. But in this puzzle, unlike a magic square, every number is included in exactly two sums. This gives us freedom we wouldn't normally have. We can pair 1 with 12 on the outside, but because of this freedom, we can put the next-most-extreme numbers together, to give us a place to start from:?????1?2?11?12
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.In a magic square, 1 and the maximum number are usually paired. But in this puzzle, unlike a magic square, every number is included in exactly two sums. This gives us freedom we wouldn't normally have. We can pair 1 with 12 on the outside, but because of this freedom, we can put the next-most-extreme numbers together, to give us a place to start from:?????1?2?11?12There is one undetermined number in a sum with 11 and a sum with 12. That can probably be made as small as possible: 3. (We could have done this symmetrically with 1 and 2 needing a big number, but probably not both at the same time.)
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.In a magic square, 1 and the maximum number are usually paired. But in this puzzle, unlike a magic square, every number is included in exactly two sums. This gives us freedom we wouldn't normally have. We can pair 1 with 12 on the outside, but because of this freedom, we can put the next-most-extreme numbers together, to give us a place to start from:?????1?2?11?12There is one undetermined number in a sum with 11 and a sum with 12. That can probably be made as small as possible: 3. (We could have done this symmetrically with 1 and 2 needing a big number, but probably not both at the same time.)?????1?2311?12
These kinds of problems are special because we're only looking for one solution, so that we can make educated guesses to stumble upon one.In a magic square, 1 and the maximum number are usually paired. But in this puzzle, unlike a magic square, every number is included in exactly two sums. This gives us freedom we wouldn't normally have. We can pair 1 with 12 on the outside, but because of this freedom, we can put the next-most-extreme numbers together, to give us a place to start from:?????1?2?11?12There is one undetermined number in a sum with 11 and a sum with 12. That can probably be made as small as possible: 3. (We could have done this symmetrically with 1 and 2 needing a big number, but probably not both at the same time.)?????1?2311?12To complete 3+12, we need a sum of 11, which we could only get as 6+5 or 7+4. To complete 3+11, we need 5+7 or 4+8. Therefore, we can't pick 7+4 because it would wipe out both possibilities to complete the diagonal (this feels like kakuro). As such, the row needs a 6 and a 5. Which should go in the bottom left corner? Probably the middling value 6 since it's in a sum with 1 and a sum with 12: