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beaker
Posted on: Fri Dec 06, 2019 1:25 am
Posts: 707 Location: Ladysmith, BC, Canada Joined: Fri May 13, 2011 1:37 am

1 to +4 puzzle
Is there a "table" of possible combinations that would help in solving a 1 to +4 puzzle on this site? I ask because my latest bonus puzzle is one of this type and I have spent almost 4 hours trying to solve it and never get close to a solution




clm
Posted on: Fri Dec 06, 2019 12:00 pm
Posts: 762 Joined: Fri May 13, 2011 6:51 pm

Re: 1 to +4 puzzle
beaker wrote: Is there a "table" of possible combinations that would help in solving a 1 to +4 puzzle on this site? I ask because my latest bonus puzzle is one of this type and I have spent almost 4 hours trying to solve it and never get close to a solution Hi, beaker. First my congratulations for your constancy and interest to solve the more difficult puzzles. The is not a table, as far as I know. I have seen some of these in the books IIRC, but no one provided a step by step solution in the forum. And, in fact, there are different types like 2 to 3, 4 to 4, 1 to 7, etc.. The main problem is generally related to the subtraction cages, since the order of the operators may vary and that tends to confuse (you must consider all permutations, even starting in a negative number, while with positive integers you always depart from the higher number, then having less possibilities). Usually, the clues for this type, for instance in the 1 to 4, should be to study the position of the numbers 0, 3 and 2. Perhaps if Patrick provides that puzzle (I assume you did not make a printout) we could help or propose some tip. Best, clm.




beaker
Posted on: Fri Dec 06, 2019 7:46 pm
Posts: 707 Location: Ladysmith, BC, Canada Joined: Fri May 13, 2011 1:37 am

Re: 1 to +4 puzzle
It is still available........I can print it out but then I do not know how to post the screen shot




jaek
Posted on: Sat Dec 07, 2019 2:08 am
Posts: 261 Joined: Fri Jun 17, 2011 8:15 pm

Re: 1 to +4 puzzle
beaker wrote: It is still available........I can print it out but then I do not know how to post the screen shot I'm a little confused by your wording. If you took a screen shot then you can go to imgur.com, click on "new post" and then upload the picture. Patrick linked to more complete instructions for this earlier today. If you need help taking a screen shot then I'd suggest doing a search for how to take a screen shot with your operating system. I know you want to sort this out before you lose out on your next possible bonus becomes available so good luck.




beaker
Posted on: Sat Dec 07, 2019 3:52 am
Posts: 707 Location: Ladysmith, BC, Canada Joined: Fri May 13, 2011 1:37 am

Re: 1 to +4 puzzle
where is the Patrick instructions......I am not that computer literate......too late as the 4 timed [color=#BF0000]points put me past point of no return.[/color].....someday I will have to find out the "imgur" procedure.....I have spent over 6 hours in the last 24 with this puzzle......am glad it is gone and I can quit obsessing about it (my 75 year old brain just would not let go of it).......sigh of relief




clm
Posted on: Sat Dec 07, 2019 11:35 am
Posts: 762 Joined: Fri May 13, 2011 6:51 pm

Re: 1 to +4 puzzle
beaker wrote: where is the Patrick instructions......I am not that computer literate......too late as the 4 timed [color=#BF0000]points put me past point of no return.[/color].....someday I will have to find out the "imgur" procedure.....I have spent over 6 hours in the last 24 with this puzzle......am glad it is gone and I can quit obsessing about it (my 75 year old brain just would not let go of it).......sigh of relief Hi, beaker. Here is the full solution. First, we observe that cages a1a2 and b2b3 can only have 1 and 1 as candidates (the only way of having a sum of 0). With all positive numbers (including the 0) and no 1 in, cage 8+ only admits (4,4,0), (3,3,2) or (2,2,4). The case (4,4,0) is inmediately eliminated since you would have a 0 in b6 and then the 2 in a5 is not possible. The case (2,2,4) is not possible since the 3 goes to a6 (>>> b6 = 0 and then a 0 is not possible in a5). Consequently 8+ must be (3,3,2). The cage 1 in f3f4 should be (1,0), (0,1), (1,2), (2,3) or (3,4) (distance of 1 between the two candidates). Obviously, since the 0 is not possible (cage 0: up), only (1,2) is valid, then f3=2 and f4 = 1. The cage 3+ (bottom right) can not contain a 0 or a 2. Additionally the 4 is not valid inside (because it would require 1 and 0 to add to +3), then only 1, 1 and 3 are inside (all different, it's not possible to repeat any of them), so we place a 1 in e6 and the pair (1,3) as candidates in f5f6 >>> cage 0: is (0,4). Adding numbers in columns d and e (total sum of 20) we find that d4d5 must sum 1, so this pair is (0,1) and then d5 = 1 and d4 = 0. Now cage 3+ in e4e5 has the candidates (1,4) [only this option, because (0,3) or (1,2) are not valid]. A 3 in d1 is not possible since to have a sum of 3 in e1e2 you would require (1,4) or (0,3) or (1,2) and no one is possible. Then d2 = 3 and now, to complete 7+, d3 = 4 and e3 = 0. Consequently d1 = 1, e1 = 3 and e2 = 2. An we complete the two cages 0+ with a1 = 1 (a2 = 1) and b2 = 1 (b3 = 1). Then c3 = 1. Next is to see that a 3 must be inside the 3cell cage 2, so a 0 must be the third candidate (it's quickly seen that other numbers are not possible: 4, 2 or 1). With (0,3) in c5c6 >>> b1 = 0 >>> a6 = 0 >>> a5 = 4 >>> b5 = 2. Adittionally b6 = 4. And f2 = 0, f1 = 4, c1 =2, c2 = 4. An the rest is straight forward: c4 = 1, e4 = 4, e5 = 1, f5 = 3, f6 = 1, c5 = 0 and c6 = 3. Now, let's see if either Patrick or yourself can upload the puzzle pnm: here it is ^^^




beaker
Posted on: Sat Dec 07, 2019 11:46 pm
Posts: 707 Location: Ladysmith, BC, Canada Joined: Fri May 13, 2011 1:37 am

Re: 1 to +4 puzzle
Has any one followed the logic of clm.......only one question is that if d1 = 1 and 2e = 3 and e2 = 2, then how is it possible to add 3,2,1 and get 6.....or did I read the sequence wrong




clm
Posted on: Sun Dec 08, 2019 12:50 am
Posts: 762 Joined: Fri May 13, 2011 6:51 pm

Re: 1 to +4 puzzle
beaker wrote: Has any one followed the logic of clm.......only one question is that if d1 = 1 and 2e = 3 and e2 = 2, then how is it possible to add 3,2,1 and get 6.....or did I read the sequence wrong Yes, you are right, thank you, beaker, the development is wrong from "Adding numbers in columns d and e ... ", the reason being that two columns do not sum 20, in this case, due to the presence of a 1, so the sum is 9 per column, that is, 18 in total. I did it to quickly, I apologize for that, , tomorrow I will correct from that point on.




clm
Posted on: Sun Dec 08, 2019 1:41 am
Posts: 762 Joined: Fri May 13, 2011 6:51 pm

Re: 1 to +4 puzzle
The corrected development is this one: First, we observe that cages a1a2 and b2b3 can only have 1 and 1 as candidates (the only way of having a sum of 0). With all positive numbers (including the 0) and no 1 in, cage 8+ only admits (4,4,0), (3,3,2) or (2,2,4). The case (4,4,0) is inmediately eliminated since you would have a 0 in b6 and then the 2 in a5 is not possible. The case (2,2,4) is not possible since the 3 goes to a6 (>>> b6 = 0 and then a 0 is not possible in a5). Consequently 8+ must be (3,3,2). The cage 1 in f3f4 should be (1,0), (0,1), (1,2), (2,3) or (3,4) (distance of 1 between the two candidates). Obviously, since the 0 is not possible (cage 0: up), only (1,2) is valid, then f3=2 and f4 = 1. The cage 3+ (bottom right) can not contain a 0 or a 2. Additionally the 4 is not valid inside (because it would require 1 and 0 to add to +3), then only 1, 1 and 3 are inside (all different, it's not possible to repeat any of them), so we place a 1 in e6 and the pair (1,3) as candidates in f5f6 >>> cage 0: is (0,4). Adding numbers in columns d and e (total sum of 18) we find that d4d5 must sum 1, so this pair is (1,0). Cage 6+, not having 0's inside, could be (1,1,4) (which is not valid due to e6 = 1) or (1,2,3) or (4,3,1). Now we observe that d3 is not a 1 because it would require d2e3 to be either (2,4) or (3,3) both impossible. Similarly d2 can not be a 1 since it would require d3e3 to be (2,4). Than d1 = 1, so cage 6+ is (1,2,3) and e1e2 = (2,3). We can fill now a1 = 1, a2 = 1, b2 = 1, b3 = 1, d2 = 3, d3 = 4, e3 = 0 and c3 = 1. Also cage 3+ is (1,4), and certainly e1 = 3 and e2 = 2. In row 6, f6 = 1 and f5 = 3. Next is to see that, in column c, c5 = 1 and c6 = 3. And this forces to select d5 = 0 (and not 1) to comply with the 3cell cage 2. Consequently d4 = 1, e4 = 4 and e5 = 1. An the rest is straight forward: a5 = 4, b5 = 2, a6 = 0, b6 = 4, b1 = 0, f1 = 4, f2 = 0, c1 = 2 and c2 = 4. The solution, then, is: 1 0 2 1 3 4 1 1 4 3 2 0 3 1 1 4 0 2 2 3 0 1 4 1 4 2 1 0 1 3 0 4 3 2 1 1




beaker
Posted on: Sun Dec 08, 2019 6:03 am
Posts: 707 Location: Ladysmith, BC, Canada Joined: Fri May 13, 2011 1:37 am

Re: 1 to +4 puzzle
Curious to know from other users if they have had one of these as a bonus configuration (1 to +4)..........if not LOOK OUT!!! Now, I can put this, finally, behind me....THANK YOU, clm






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