Pi Day Puzzle: Solve For Each Letter

This is a fun little problem, can you solve it?

The problem is from Manan Shah's website Math Misery? which has many fun problems. Check his website out:

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[isaacaguilar]

Damn bruh. I misunderstood. I thought it was P times I

[harrytsang]

P, I, E = 1, 6, 9

Sqrt(16)+9=sqrt(169)=13

Special thanks to the high school teacher that made me memorize the squares from 11 to 20

[sabersworn]

169 was the first number I tried plugging in :|

[vdang]

I thought PI meant P * I, and PIE meant P * I * E, and deduced that E must be 1, 4 or 9, and found two solutions (2, 8, 4) and (8, 2, 4) for (P, I, E) :)

[skifast_takechances]

You can actually algebraically solve this by taking the obvious step: square both sides. Easily, we get E = 9. Plugging in and letting sqrt(10P + I) = x, we get x^2 - 2x - 8 = 0, => x = 4 => P = 1, I = 6

[dilipgupta]

In this question I tried to find out a perfect square of 3 digit number and the least was 169. Hence I solved the answer by trial and error method

[harrywang]

You said no calculators but you never said anything about searching for the answer online

[nayutaito]

If PI is not perfect square:
is not an integer, but (sqrt(PIE))^2=PIE is an integer, so it leads to the contradiction.

[lamcho]

Lol, solved this just because 169 is the largest square I could remember.

[jrsbenevides]

A more algebraic solution would be: Making PI = k², you'll end up with the following equation: 9k² - 2kE - E² + E = 0. Computing delta, yields in 40E²-36E, or 4E(10E-9), which has a perfect solution for 1 and 9, but only E=9 returns a natural solution for k, which is k=4. Therefore, k² = 16 --> PI = 16 --> P = 1 and I = 6.

[teisanumihai]

Wait for 14 March. Then...




Happy Pi day!!! 🎂🎉🎉

[knetknecht]

I'm a bit proud of myself, because I didn't have to solve this problem with any formula.
I just, ,saw" the solution after like a minute of thinking
sqrt(16) +9= sqrt(169)

[Tiqerboy]

This one was easy for me to solve since there's a bridge near where I live and its clearance is marked by a sign 16'9". I noticed 16, 9 and 169 are all perfect squares.

[SomeGuyx]

√16 + 9 = √169
(4 + 9 = 13)
P=1, I=6, E=9
I did it in my head in under a minute, without touching a calculator, and I used the same exact logic you did, with having both PI and PIE be perfect squares.

[AAAAAA-gjdi]

I don't know about how many solutions this has
But √16 + 9= √169. Easy but good. Took almost 30secs. Hmm, challenging😄

Both the terms of Left hand side of the equation can not be greater than 9. So the LHS<= 18, i.e. PIE<= 324. We are only left with 2 possibilities 16 and 25.😅

[yourlordandsaviouryeesusbe]

Haven't watched the solution, but I found P=2, I=8, E=4 is a solution.
√(2×8) + 4 = √(2×8×4)

[ln-physics]

You know what pizza exactly means.

The volume of a solid cylinder having radius z and height a
pi×z×z×h

[flochforster]

I feel so proud of myself for figuring it out!! I did Google the 2-digit and 3-digit squares though. Could have programmed an Excel spreadsheet for it but I was lazy haha

[mgerry]

You don't have to list all the squares up to 999. The highest possible value for PI is 81, whose square root is 9, and let's assume that E's highest possible value is also 9. So the greatest value we can get on the left hand side is 18. Thus, the greatest value underneath the square root on the right hand side can be at most 18^2=324.

[matveyschannel]

You can shorten your search, as you can prove that PI <= 20