Number Puzzle: Solve 34 in 11 Lines Using 1-17

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Discussion Overview

The discussion revolves around a number puzzle that requires participants to arrange the numbers 1 to 17 in such a way that the sum of the numbers on each of 11 lines equals 34. The conversation includes attempts to solve the puzzle and verify proposed solutions.

Discussion Character

  • Exploratory, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant claims to have a solution to the puzzle, describing it as challenging.
  • Another participant points out a potential error in a proposed solution, stating that the sum of 10, 2, and 12 does not equal 34.
  • A participant suggests that there are only two symmetrical solutions to the puzzle, implying a uniqueness in the arrangement.
  • One participant asserts that their solution matches another's exactly, suggesting a singularity in the solution.

Areas of Agreement / Disagreement

There is disagreement regarding the correctness of specific solutions, with some participants questioning the validity of proposed sums while others assert the uniqueness of their solutions.

Contextual Notes

Participants have not resolved the mathematical steps leading to their claims, and there are assumptions about the symmetry and uniqueness of solutions that remain unverified.

Helios
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Using the numbers 1 - 17, place the numbers in the circles so that the sum of the numbers on every line equals 34. There are 11 lines. I have one solution. I think this is a very challenging puzzle that few can solve.
 

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Mathematics news on Phys.org
Hi Helios!
From top to down, and left to right:
13
4,7,17,6
9,1
5,3
11,8,15
16,14
10,2,12
:smile:
 
As far as I can tell 10+2+12 in bottom line is not 34...

Seems to me like there are just two solutions - symmetrical, so in a way there exist only one.

14 - 16 4 8 6 - 3 1 - 13 11 - 5 17 12 - 7 2 - 10 9 15

(these are rows)
 
Last edited:
Borek's solution is an exact match to mine. This solution looks unique. Thanks all for your efforts with this puzzle.
 

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