Glyn wrote:If the puzzle is unique as it is, ie no more givens are required, does the 5 letter word describe an extra constraint?

Instead of "extra", try "only".

Interesting my next effort is 5 letter word is FORTY or FIFTY.

I used these numbers as a constraint on the sum of a diagonal.

Applying that and ignoring solutions where additional information beyond the word would be required.

I have 6 solutions where a diagonal sums to 40.

I have one solution where a diagonal sums to 50.

Here it is :-

Diagonal SW-NE = 7+1+8+4+5+6+2+8+9 = 50.

The word is FIFTY

This is my 'true' answer.

Edit: I now think 'false' answer is:-

Only a missing '8' added at r9c9 leads to a unique solution.

Unfortunately I can't see a quick reason to pick that in advance. (Best so far is given 8's share a box with given 7's and a row with given 3's but if I include a column requirement it would suggest given 2's lock the missing 8 in r9c7).

I used these numbers as a constraint on the sum of a diagonal.

Applying that and ignoring solutions where additional information beyond the word would be required.

I have 6 solutions where a diagonal sums to 40.

I have one solution where a diagonal sums to 50.

Here it is :-

- Code: Select all
`.------.------.------.`

| 5 7 4| 8 6 2| 1 3 9|

| 1 2 9| 3 4 7| 5 8 6|

| 6 8 3| 5 9 1| 2 4 7|

:------+------+------:

| 3 5 1| 2 7 6| 8 9 4|

| 4 9 7| 1 5 8| 3 6 2|

| 8 6 2| 4 3 9| 7 1 5|

:------+------+------:

| 2 4 8| 9 1 5| 6 7 3|

| 9 1 6| 7 2 3| 4 5 8|

| 7 3 5| 6 8 4| 9 2 1|

'------'------'------'

Diagonal SW-NE = 7+1+8+4+5+6+2+8+9 = 50.

The word is FIFTY

This is my 'true' answer.

Edit: I now think 'false' answer is:-

- Code: Select all
`.------.------.------.`

| 5 7 4| 8 6 2| 1 3 9|

| 1 2 9| 3 4 7| 5 8 6|

| 6 8 3| 5 9 1| 2 4 7|

:------+------+------:

| 3 1 5| 2 7 6| 8 9 4|

| 4 9 7| 1 5 8| 3 6 2|

| 8 6 2| 4 3 9| 7 1 5|

:------+------+------:

| 2 4 8| 9 1 5| 6 7 3|

| 9 5 6| 7 8 3| 4 2 1|

| 7 3 1| 6 2 4| 9 5 8|

'------'------'------'

Only a missing '8' added at r9c9 leads to a unique solution.

Unfortunately I can't see a quick reason to pick that in advance. (Best so far is given 8's share a box with given 7's and a row with given 3's but if I include a column requirement it would suggest given 2's lock the missing 8 in r9c7).

- Glyn
**Posts:**357**Joined:**26 April 2007

coloin wrote:I didnt know what language the word was either.

Googling "ricis" produced many results though.

coloin wrote:but r1c1 = 5 solves the puzzle

It doesn't. My solver said placing r1c1=5 still leaves 56 solutions.

Glyn wrote:Interesting my next effort is 5 letter word is FORTY or FIFTY.

I used these numbers as a constraint on the sum of a diagonal.

Applying that and ignoring solutions where additional information beyond the word would be required.

...

The word is FIFTY

This is my 'true' answer.

Your 'true' answer is WRONG. Nice effort though, but not even close. See the hint at the end of this post.

Glyn wrote:Edit: I now think 'false' answer is:-

- Code: Select all
`.------.------.------.`

| 5 7 4| 8 6 2| 1 3 9|

| 1 2 9| 3 4 7| 5 8 6|

| 6 8 3| 5 9 1| 2 4 7|

:------+------+------:

| 3 1 5| 2 7 6| 8 9 4|

| 4 9 7| 1 5 8| 3 6 2|

| 8 6 2| 4 3 9| 7 1 5|

:------+------+------:

| 2 4 8| 9 1 5| 6 7 3|

| 9 5 6| 7 8 3| 4 2 1|

| 7 3 1| 6 2 4| 9 5 8|

'------'------'------'

Only a missing '8' added at r9c9 leads to a unique solution.

Unfortunately I can't see a quick reason to pick that in advance. (Best so far is given 8's share a box with given 7's and a row with given 3's but if I include a column requirement it would suggest given 2's lock the missing 8 in r9c7).

Congrats! You've unlocked the "fake solution". Great job!

The reason behind the missing 8 @ r9c9 is:

Count the clues carefully, band by band (3 rows) and stack by stack (3 columns). In each band and each stack there is one each of {12346789}. The only exception is the bottom band and the rightmost stack, each lacking an 8. Therefore to complete the pattern you need to place an 8-clue in b9, the bottom right block. Of all the cells there, only r9c9=8 gives a unique solution, all other placements lead to no solution or multiple solutions.

But it's just the "fake solution". Let's focus on the real one!

Triple click to see the hint on the 'real solution' I wrote:If you know the 5-letter keyword, it probably takes you about 30 seconds to fill out the whole grid, by hand using pen & paper.

- udosuk
**Posts:**2698**Joined:**17 July 2005

udosuk Triple click wrote:Divide and conquer.

Does it involve division?

udosuk Triple click wrote:1. What you see is NOT what you get. (Looks can be deceiving.)

2. Why are the positions of the 5s not given in the grid?

1) Not a Sudoku?

2) Because there aren't any?

- Glyn
**Posts:**357**Joined:**26 April 2007

Glyn wrote:Does it involve division?

It doesn't involve division, multiplication or subtraction.

Glyn wrote:1) Not a Sudoku?udosuk Triple click wrote:1. What you see is NOT what you get. (Looks can be deceiving.)

Finally! Keep in mind this is a brainteaser/riddle, not a logical puzzle!

Glyn wrote:2) Because there aren't any?udosuk Triple click wrote:2. Why are the positions of the 5s not given in the grid?

There are the same number of 5s in the solution grid as any other digit from 1 to 9. However if I give as many as two 5s as clues it would become almost too easy to solve.

This riddle from 2 years ago might shred you some lights (but mine's a totally different riddle).

udosuk Triple click wrote:Divide and conquer.

With this I mean, if you can't tackle the whole thing, chop it off into pieces and tackle them one by one.

- udosuk
**Posts:**2698**Joined:**17 July 2005

Yay! The riddles are back!

Don't have a clue about the 5-letter word yet, but here's some observations:

In each box the middle cell is empty, all even digits are in one of the corners and all odd digits are in the middle cell of the sides.

So it does involve addition? In each box, givens in the opposite cells around the middle cell add up to 10.

Because the puzzle has something to do with symmetry within the boxes that places digit 5 in the middle cell of each box?

Assuming my observations have something to do with the solution, I can advance the puzzle this far:

Given the constraints mentioned above, the puzzle still has 32768 solutions, so there must be some more... The missing constraint could be that in each box, all rows, columns and diagonals add up to 15. Which gives this solution:

Aargh, the solution was too obvious...

Magic

RW

udosuk wrote:This is the "riddle":

- Code: Select all
`+---+---+---+`

|..4|8..|.3.|

|1..|..7|...|

|6..|.9.|2..|

+---+---+---+

|...|2.6|.94|

|..7|...|...|

|8..|.3.|.1.|

+---+---+---+

|2..|.1.|67.|

|9..|...|...|

|.3.|..4|...|

+---+---+---+

Don't have a clue about the 5-letter word yet, but here's some observations:

In each box the middle cell is empty, all even digits are in one of the corners and all odd digits are in the middle cell of the sides.

udosuk wrote:It doesn't involve division, multiplication or subtraction.

So it does involve addition? In each box, givens in the opposite cells around the middle cell add up to 10.

udosuk wrote:2. Why are the positions of the 5s not given in the grid?

Because the puzzle has something to do with symmetry within the boxes that places digit 5 in the middle cell of each box?

Assuming my observations have something to do with the solution, I can advance the puzzle this far:

- Code: Select all
`+---+---+---+`

|..4|81.|.38|

|159|357|.5.|

|6..|.92|27.|

+---+---+---+

|..2|276|.94|

|357|.5.|.5.|

|8..|438|61.|

+---+---+---+

|27.|61.|67.|

|951|.5.|.5.|

|.38|.94|.34|

+---+---+---+

udosuk wrote:This grid as a "puzzle" have one unique solution as it is. If you figure out what that solution is then you can find the five-letter word as the answer.

Given the constraints mentioned above, the puzzle still has 32768 solutions, so there must be some more... The missing constraint could be that in each box, all rows, columns and diagonals add up to 15. Which gives this solution:

- Code: Select all
`+---+---+---+`

|834|816|438|

|159|357|951|

|672|492|276|

+---+---+---+

|492|276|294|

|357|951|753|

|816|438|618|

+---+---+---+

|276|618|672|

|951|753|159|

|438|294|834|

+---+---+---+

Aargh, the solution was too obvious...

Magic

RW

- RW
- 2010 Supporter
**Posts:**1000**Joined:**16 March 2006

RW wrote:Yay! The riddles are back!

Yay! And the legendary RW is back too!

RW wrote:

- Code: Select all
`+---+---+---+`

|834|816|438|

|159|357|951|

|672|492|276|

+---+---+---+

|492|276|294|

|357|951|753|

|816|438|618|

+---+---+---+

|276|618|672|

|951|753|159|

|438|294|834|

+---+---+---+

Aargh, the solution was too obvious...

Magic

And with a stroke of mastery RW has completely cracked the real solution and found the magical keyword. Now it's your turn to tease our brains!

- udosuk
**Posts:**2698**Joined:**17 July 2005

Thanks udosuk! I'll continue with something that looks similar. This time I'm looking for a shorter word:

What am I

RW

- Code: Select all
`.1...9.6..58.7..23...2....8327......4....6..9...5......9.4...5..3....6......2.8..`

*-----------*

|.1.|..9|.6.|

|.58|.7.|.23|

|...|2..|..8|

|---+---+---|

|327|...|...|

|4..|..6|..9|

|...|5..|...|

|---+---+---|

|.9.|4..|.5.|

|.3.|...|6..|

|...|.2.|8..|

*-----------*

What am I

RW

- RW
- 2010 Supporter
**Posts:**1000**Joined:**16 March 2006

Obviously, decimals of PI :

so, the answser could be PI

JPF

- Code: Select all
`.1...9.6..58.7..23...2....8327......4....6..9...5......9.4...5..3....6......2.8..`

3,14159265358979323846264338327950288419716939937510582097494459230781640628620899

so, the answser could be PI

JPF

- JPF
- 2017 Supporter
**Posts:**3754**Joined:**06 December 2005**Location:**Paris, France

Wow, JPF, that was quick.

Now that the legends are coming back this place is getting more and more exciting!

I hope I don't sound sour but the idea of pi did cross my mind but I was looking if the clues could be scrambled to form the series of digits. Obviously JPF is more observant than me!

Waiting for RW's confirmation...

Now that the legends are coming back this place is getting more and more exciting!

I hope I don't sound sour but the idea of pi did cross my mind but I was looking if the clues could be scrambled to form the series of digits. Obviously JPF is more observant than me!

Waiting for RW's confirmation...

- udosuk
**Posts:**2698**Joined:**17 July 2005

JPF wrote:Obviously, decimals of PI :

- Code: Select all
`.1...9.6..58.7..23...2....8327......4....6..9...5......9.4...5..3....6......2.8..`

3,14159265358979323846264338327950288419716939937510582097494459230781640628620899

so, the answser could be PI

That is correct!! That was very quick, didn't realise it was this easy. Perhaps I shouldn't have posted the puzzle in line format, but saved that as a hint for later...

Your turn JPF!

RW

- RW
- 2010 Supporter
**Posts:**1000**Joined:**16 March 2006