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Find just one digit (Posted on 2005-11-10) Difficulty: 2 of 5
If ABC+DEF+GHI=JJJ, each letter stands for a different digit, and no number starts with zero, what is J?

See The Solution Submitted by Federico Kereki    
Rating: 4.0000 (6 votes)

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Solution Solution | Comment 1 of 13

xdog gave the mathematical reason. My solution was just brute force: 

J = 9 for every possibility

 104+ 237+ 658= 999
 104+ 238+ 657= 999
 104+ 257+ 638= 999
 104+ 258+ 637= 999
 104+ 327+ 568= 999
 104+ 328+ 567= 999
 104+ 367+ 528= 999
 104+ 368+ 527= 999
 107+ 234+ 658= 999
 107+ 238+ 654= 999
 107+ 254+ 638= 999
 107+ 258+ 634= 999
 107+ 324+ 568= 999
 107+ 328+ 564= 999
 107+ 364+ 528= 999
 107+ 368+ 524= 999
 108+ 234+ 657= 999
 108+ 237+ 654= 999
 108+ 254+ 637= 999
 108+ 257+ 634= 999
 108+ 324+ 567= 999
 108+ 327+ 564= 999
 108+ 364+ 527= 999
 108+ 367+ 524= 999
 124+ 307+ 568= 999
 124+ 308+ 567= 999
 124+ 367+ 508= 999
 124+ 368+ 507= 999
 127+ 304+ 568= 999
 127+ 308+ 564= 999
 127+ 364+ 508= 999
 127+ 368+ 504= 999
 128+ 304+ 567= 999
 128+ 307+ 564= 999
 128+ 364+ 507= 999
 128+ 367+ 504= 999
 134+ 207+ 658= 999
 134+ 208+ 657= 999
 134+ 257+ 608= 999
 134+ 258+ 607= 999
 137+ 204+ 658= 999
 137+ 208+ 654= 999
 137+ 254+ 608= 999
 137+ 258+ 604= 999
 138+ 204+ 657= 999
 138+ 207+ 654= 999
 138+ 254+ 607= 999
 138+ 257+ 604= 999
 140+ 273+ 586= 999
 140+ 276+ 583= 999
 140+ 283+ 576= 999
 140+ 286+ 573= 999
 143+ 270+ 586= 999
 143+ 280+ 576= 999
 146+ 270+ 583= 999
 146+ 280+ 573= 999
 150+ 362+ 487= 999
 150+ 367+ 482= 999
 150+ 382+ 467= 999
 150+ 387+ 462= 999
 152+ 360+ 487= 999
 152+ 380+ 467= 999
 154+ 207+ 638= 999
 154+ 208+ 637= 999
 154+ 237+ 608= 999
 154+ 238+ 607= 999
 157+ 204+ 638= 999
 157+ 208+ 634= 999
 157+ 234+ 608= 999
 157+ 238+ 604= 999
 157+ 360+ 482= 999
 157+ 380+ 462= 999
 158+ 204+ 637= 999
 158+ 207+ 634= 999
 158+ 234+ 607= 999
 158+ 237+ 604= 999
 160+ 352+ 487= 999
 160+ 357+ 482= 999
 160+ 382+ 457= 999
 160+ 387+ 452= 999
 162+ 350+ 487= 999
 162+ 380+ 457= 999
 164+ 307+ 528= 999
 164+ 308+ 527= 999
 164+ 327+ 508= 999
 164+ 328+ 507= 999
 167+ 304+ 528= 999
 167+ 308+ 524= 999
 167+ 324+ 508= 999
 167+ 328+ 504= 999
 167+ 350+ 482= 999
 167+ 380+ 452= 999
 168+ 304+ 527= 999
 168+ 307+ 524= 999
 168+ 324+ 507= 999
 168+ 327+ 504= 999
 170+ 243+ 586= 999
 170+ 246+ 583= 999
 170+ 283+ 546= 999
 170+ 286+ 543= 999
 173+ 240+ 586= 999
 173+ 280+ 546= 999
 176+ 240+ 583= 999
 176+ 280+ 543= 999
 180+ 243+ 576= 999
 180+ 246+ 573= 999
 180+ 273+ 546= 999
 180+ 276+ 543= 999
 180+ 352+ 467= 999
 180+ 357+ 462= 999
 180+ 362+ 457= 999
 180+ 367+ 452= 999
 182+ 350+ 467= 999
 182+ 360+ 457= 999
 183+ 240+ 576= 999
 183+ 270+ 546= 999
 186+ 240+ 573= 999
 186+ 270+ 543= 999
 187+ 350+ 462= 999
 187+ 360+ 452= 999
 205+ 316+ 478= 999
 205+ 318+ 476= 999
 205+ 376+ 418= 999
 205+ 378+ 416= 999
 206+ 315+ 478= 999
 206+ 318+ 475= 999
 206+ 375+ 418= 999
 206+ 378+ 415= 999
 208+ 315+ 476= 999
 208+ 316+ 475= 999
 208+ 375+ 416= 999
 208+ 376+ 415= 999
 215+ 306+ 478= 999
 215+ 308+ 476= 999
 215+ 376+ 408= 999
 215+ 378+ 406= 999
 216+ 305+ 478= 999
 216+ 308+ 475= 999
 216+ 375+ 408= 999
 216+ 378+ 405= 999
 218+ 305+ 476= 999
 218+ 306+ 475= 999
 218+ 375+ 406= 999
 218+ 376+ 405= 999
 275+ 306+ 418= 999
 275+ 308+ 416= 999
 275+ 316+ 408= 999
 275+ 318+ 406= 999
 276+ 305+ 418= 999
 276+ 308+ 415= 999
 276+ 315+ 408= 999
 276+ 318+ 405= 999
 278+ 305+ 416= 999
 278+ 306+ 415= 999
 278+ 315+ 406= 999
 278+ 316+ 405= 999

 

 

Edited on November 10, 2005, 9:22 am
  Posted by Penny on 2005-11-10 09:05:44

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