March 2025
Problem of the Month

Pi Problem
from K. Sengupta, Calcutta, India



Solve the following equation for P, I, and E, where PIE is a 3-digit number and the three digits are unique:
(Give both answers)



Solution:

PIE = 256 or 361

Here is Kamal Lohia's solution:

There are 22 3-digit perfect squares from 10² to 31². Now checking the numbers with 3 different digits, we get

13 = √169 ≠ 1•6 + 9
14 = √196 ≠ 1•9 + 6
16 = √256 = 2•5 + 6 👍🏻
17 = √289 ≠ 2•8 + 9
18 = √324 ≠ 3•2 + 4
19 = √361 = 3•6 + 1 👍🏻
23 = √529 ≠ 5•2 + 9
24 = √576 ≠ 5•7 + 6
25 = √625 ≠ 6•2 + 5
27 = √729 ≠ 7•2 + 9
28 = √784 ≠ 7•8 + 4
29 = √841 ≠ 8•4 + 1
31 = √961 ≠ 9•6 + 1

So, there are exactly two possible values of PIE: 256 & 361



Correctly solved by:

1. Kamal Lohia Hisar, Haryana, India
2. Colin (Yowie) Bowey Beechworth, Victoria, Australia
3. Davit Banana Istanbul, Turkey
4. Ivy Joseph Pune, Maharashtra, India
5. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
6. Seth Cohen Concord, New Hampshire, USA
7. Eric Erdman Northrop High School,
Fort Wayne, Indiana, USA
8. Arda Karahan Trabzon Science High School,
Trabzon Province, Turkey
9. Kelly Stubblefield Mobile, Alabama, USA



Send any comments or questions to: David Pleacher