Soldiers in row

“How to arrange 10 soldiers in 5 rows of 4 soldiers each?”

Although this problem looks impossible, this is a solution:

(16,16)

(8,8)8

(8,16)0.40(8,16) (0.3915,10.4721)0.41(0.3915,10.4721) (15.6085,10.4721)0.42(15.6085,10.4721) (3.2977,1.5279)0.43(3.2977,1.5279) (12.7023,1.5279)0.44(12.7023,1.5279)

(8,4.95)0.45(8,4.95) (10.9,7.05)0.46(10.9,7.05) (5.1,7.05)0.47(5.1,7.05) (9.8,10.45)0.48(9.8,10.45) (6.2,10.45)0.49(6.2,10.45)

Input

Input consists of several cases, each with a natural number $n$ between 2 and $10^8$ .

Output

For every case, we must arrange $n$ soldiers in rows, as follows: In a circumference, we choose $x$ different points, where $x$ is odd and at least 3. Then, we draw $x$ straight segments between different pairs of those $x$ points. At the end, we can place one soldier on every resulting intersection, those produced at the ends of the segments included.

For every given $n$ , print the minimum $x$ that allows arranging at least $n$ soldiers.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:55:32.611Z