# Happy Pi-Day! Try to solve this “PiDoku”

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
• Also, very nice and smart puzzle! – 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 ;-) – André Mar 15 '18 at 2:30
• (Clever additional challenge, but moving the goalposts makes answerers redo work they've already done once, for little gain.) – Rubio Mar 15 '18 at 4:42

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)

• 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 5:55
• @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 6:35
• @boboquack But how would you eliminate the other 2 solutions? – Ariana Mar 15 '18 at 6:36
• @Ariana the other solutions are eliminated because you have assumed there is one solution. – boboquack Mar 15 '18 at 6:37
• – Ariana Mar 15 '18 at 7:34

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