18
$\begingroup$

enter image description here

Rules

  • Arrange numbers from 1 to 15 to the white triangles.
  • A op B = result
    enter image description here
  • Green triangle means 2 numbers of its side are adjacent numbers.
  • (-) means find the difference
  • (/) means divide the bigger number with the lower number.

Example
enter image description here

$\endgroup$
  • $\begingroup$ Does each number occur once, or are we allowed to enter them multiple time? $\endgroup$ – Mike Limburg Apr 27 '17 at 6:35
  • $\begingroup$ @MikeLimburg : each number occur once $\endgroup$ – Jamal Senjaya Apr 27 '17 at 6:36
11
$\begingroup$

Following a well-designed trail of clues leads to...

           

That trail begins at the two division / triangles that both include the given 3 and must each include consecutive numbers.   The only possibilities are {2,3,6} and {3,4,12}, which fairly rapidly sift to:
• Use up 5 of the 7 available even numbers.
• Force a pattern of odd and even numbers among the remaining cells.

The 2 remaining even numbers fit only one way and:
• Daisy-chain upward to fill out all but the bottom row.
• Leave a set of numbers with only one pair that can produce consecutive numbers in the bottom right triangle.

The bottom left corner shakes out from there. (And, yeah, the original path to solution involved some unnecessary trial and error.)

$\endgroup$
  • $\begingroup$ I hit the answer button, write the text "This is my solution", copy the picture from my local machine, then PSE says an answer was just added. I swear a lot, check the solution, is the same as what I found, swear again then upvote. Then swear again. Good job. ##@!#@(*&@# (censored) $\endgroup$ – Marius Apr 27 '17 at 6:59
  • 1
    $\begingroup$ OOOOOOOOOOooooo, Marius! You can be sure it has gone the other way, too, for both of us no doubt. $\endgroup$ – humn Apr 27 '17 at 7:00
  • $\begingroup$ @humn : Still waiting for your logic explanation. $\endgroup$ – Jamal Senjaya Apr 27 '17 at 7:03
  • 1
    $\begingroup$ Very funny, @Jamal Senjaya, another very well clued puzzle in any case, by the way $\endgroup$ – humn Apr 27 '17 at 7:04
  • $\begingroup$ @humn : Thank you, I will try to create many more. $\endgroup$ – Jamal Senjaya Apr 27 '17 at 7:08
5
$\begingroup$

You actually get to the same solution with more work even if you don't read what green triangles mean.

That 3 you can see can be a part of (6, 2), (12, 4) and (15, 5) if you forget about green triangle rule. Due to subtraction below, 15, 5 cannot be on the bottom and (12,4) could be only if there is (14, 2) or (13, 1) below. Now if 12 is on the right, it would require +3 to make 15 = not possible, so 12 would need to be on the left. There is a plus sign too, so either 13 or 14 appears on the top and both 1 and 2 are used, meaning the other pair has to be (15, 5), and 11 is there on the right. Now, say there is 13 below - it needs 1 to make 12 and 9 to make 4 (14 would need 2 and 10). But to make 1 out of 2, or 2 out of 1, you need number 3, which is already used.

So, we have

6 and 2 are below 3. We have 3 options for the other division and that subtraction: (bottom towards top)
6, 2, 10; 3, 12; 4
6, 2, 13; 3, 15; 5
2, 6, 9; 3, 15; 5

Let's start with the last one:

6 cannot be made as 7-1, as you will not be able to use 7. (7+2 or 7-5 both duplicate a number). It cannot be made as 8-2, 9-3, 11-5, 12-6 obviously and 13-7 is eliminated for the same reason as 7-1. 10-4 has the problem of making 9 which would require 4+5. So, 14-8 is the only option. Bottom right is 1, then 8, then 14, then 12 - to make 2. We have 4, 7, 10, 11, 13 left. But we cannot make top right corner - no 2 numbers are 5 apart. OK, so this option is eliminated.

Next:

Let's consider 6, 2, 13 now. Under 2 we could have (7, 9) => 1, 7, 9, 4, (8, 10) => impossible, (9, 11) => impossible, (10, 12) => 4, 10, 12, 1 or (12, 14) => 8, 14, 12, 1.

Now:

First option leads to 8, 10, 11, 12, 14 for remaining numbers, which again doesn't have a gap of 5. Second one has 7, 8, 9, 11, 14. So, 14 on the top, 9 to the left of 5. We would need 12 to make that 9 and we don't have it. Too bad. And the third ends up with 4, 7, 9, 10, 11. 9 on top, 4 under it, 7 next. And now we require 1 which we don't have. So, this doesn't work either.

Finally:

We know the central part of the whole triangle is 6, 2, 10; 3, 12; 4. Now, how to make 10? (1, 9) is the only option. (2, 8), (3, 7) and (4, 6) are impossible. 9 needs to be right with 1 on the left or we won't make 2. Fill in 13, 7 to make 2 and 6. Note that remaining numbers are 5, 8, 11, 14, 15. To have difference of 4, 15 on top and 11 below are required. 14 to make 11, 8 to make 14 and 5 to make 8, and we have our unique solution.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.