## Squares with the same digits

A study of square numbers up to 10^5 has revealed that …

… there is only one set of six squares that have the same digits:

103^2 = 10609     130^2 = 16900     140^2 = 19600
247^2 = 61009     301^2 = 90601     310^2 = 96100

… there is one set of five squares that have the same digits:

128^2 = 16384     178^2 = 31684     191^2 = 36481
196^2 = 38416     209^2 = 43681

… there are two sets of four squares that have the same digits:

102^2 = 10404     120^2 = 14400
201^2 = 40401     210^2 = 44100

133^2 = 17689     137^2 = 18769
281^2 = 78961     286^2 = 81796

… there are nine sets of three squares that have the same digits:

13^2 = 169     14^2 = 196     31^2 = 961

36^2 = 1296     54^2 = 2916     96^2 = 9216

108^2 = 11664     129^2 = 16641     204^2 = 41616

112^2 = 12544     211^2 = 44521     229^2 = 52441

135^2 = 18225     159^2 = 25281     285^2 = 81225

148^2 = 21904     203^2 = 41209     302^2 = 91204

154^2 = 23716     181^2 = 32761     269^2 = 72361

160^2 = 25600     245^2 = 60025     250^2 = 62500

207^2 = 42849     222^2 = 49284     288^2 = 82944

… there are 30 pairs of squares that have the same digits

we exclude trivial solutions such as   (100, 001),   (400,004),   etc.

12^2 = 144         21^2 = 441

16^2 = 256         25^2 = 625

32^2 = 1024         49^2 = 2401

33^2 = 1089         99^2 = 9801

37^2 = 1369         44^2 = 1936

42^2 = 1764         69^2 = 4761

64^2 = 4096         98^2 = 9604

101^2 = 10201         110^2 = 12100

106^2 = 11236         146^2 = 21316

113^2 = 12769         311^2 = 96721

122^2 = 14884         221^2 = 48841

144^2 = 20736         174^2 = 30276

152^2 = 23104         179^2 = 32041

153^2 = 23409         198^2 = 39204

155^2 = 24025         205^2 = 42025

157^2 = 24649         158^2 = 24964

166^2 = 27556         275^2 = 75625

172^2 = 29584         233^2 = 54289

186^2 = 34596         213^2 = 45369

190^2 = 36100         251^2 = 63001

202^2 = 40804         220^2 = 48400

192^2 = 36864         294^2 = 86436

206^2 = 42436         208^2 = 43264

216^2 = 46656         258^2 = 66564

224^2 = 50176         226^2 = 51076

225^2 = 50625         255^2 = 65025

228^2 = 51984         309^2 = 95481

266^2 = 70756         274^2 = 75076

273^2 = 74529         282^2 = 79524

314^2 = 98596         316^2 = 99856