Happy Pi-Day! Try to solve this "PiDoku"

Question

To celebrate the Pi-Day (3/14) adequately, a challenging math puzzle must not be missing.

Rules:

Fill in the numbers 1-9 exactly once in every row, column, and region.
On top of that, you need to use $\pi$ exactly three times in every row, column and region to fill in the remaining gaps.

What's the solution for this $\pi$doku?

Additional challenge: Try to find a "creative way" to write Pi each time you're using it! For example: $4\cdot\left(\left(\frac{1}{2}\right)!\right)^2$

Welcome to PSE! Do take a look at the tour page to acquaint yourself with the site, and earn a badge. — Phylyp, Mar 14 '18 at 17:27
I got to be the 3rd upvote for the below answer, and the 14th for the (awesome) puzzle - seems quite fitting for today :) — puzzledPig, Mar 14 '18 at 20:40
I added an additional challenge for those of you, who felt bored while solving this puzzle ;-) — NAMELESS, Mar 15 '18 at 02:30
(Clever additional challenge, but moving the goalposts makes answerers redo work they've already done once, for little gain.) — Rubio, Mar 15 '18 at 04:42
@Rubio I'm sorry. I will keep that in mind for future posts! — NAMELESS, Mar 15 '18 at 11:48
@AndréDalwigk If we let this one slide, I'd be more than happy to oblige with your additional request ;) . — Discrete lizard, Mar 15 '18 at 20:15
I'm toying with the idea of publishing another PiDoku with the additional challenge stated above. Opinions? — NAMELESS, Mar 31 '18 at 00:13

score 34 · Accepted Answer · answered Mar 14 '18 at 21:54

34

For the sake of completeness, there are actually 3 possible solutions. Using process of elimination and deduction can get you to this point:

One solution is given by Sid already:

But two more are:

(Notice the threes stay put, but the nines, pis, and all but 1 five move)

and:

(Notice the threes and fives in the middle are flipped)

answered Mar 14 '18 at 21:54

gnovice

8,083
1
28
52

2

If we impose the condition that there can only be one solution. R9C7 has 3 options - 3,5,9; R8C9, R6C9 and R6C9 only has 2 options - 3,5. Thus to avoid having a rectangle containing 3 and 5s(which results in 2 solutions), R9C7 has to be 9 – Ariana Mar 15 '18 at 05:55
3

@Ariana If we impose the condition that there can only be one solution, take any of the above solutions and you're done. – boboquack Mar 15 '18 at 06:35
@boboquack But how would you eliminate the other 2 solutions? – Ariana Mar 15 '18 at 06:36
3

@Ariana the other solutions are eliminated because you have assumed there is one solution. – boboquack Mar 15 '18 at 06:37
@boboquack Maybe the initial comment was somewhat ambiguous, what it meant was during the solving process, if we assume that only one solution can exist, then we get the first one, else, we'll get all 3. – Ariana Mar 15 '18 at 06:44
1

Let us continue this discussion in chat. – Ariana Mar 15 '18 at 07:34
Congratulations! Thank you for your additional solutions. Well done! $\color{green}{\checkmark}$ – NAMELESS Mar 16 '18 at 14:18

score 30 · Answer 2 · answered Mar 14 '18 at 20:30

30

Here's the solution: I will provide the explanations within the next 24 hours because now I have to go to bed.

answered Mar 14 '18 at 20:30

Sid

15,153
2
43
94

Happy Pi-Day! Try to solve this "PiDoku"

2 Answers2