lunes, 13 de junio de 2016

Multiples with all the digits

Find for each prime, the sequence of multiples of this prime with the least sum, which contains each of the digits from 0 to 9, one and only one time.

Examples 

For 2 :  14, 36, 58, 70, 92. Sum = 270
For 3 :  12, 39, 48, 57, 60. Sum = 216
For 5 :  12345, 67890      . Sum = 80235

For 7 :  63, 70, 189, 245  . Sum = 567
For 11: 165, 704, 2398    . Sum = 3267



Can you check if this secuences are that with the least sum ?
Can you find the sequences for larger primes?


Update: Mmonchi and Vicente found this values

For 3: 6, 9, 18, 27, 30, 45 (135)
For 5: 13685, 24790 (38475) Mmonchi
For 7: 7, 28, 49, 63, 105 (252) Mmonchi
For 11: 264,539,1078 (1881)  Vicente
For 13: 26, 78, 195, 403 (702) Mmonchi
For 17: 34, 85, 102, 697 (918) Mmonchi
For 19: 19, 76, 285, 304 (684) Mmonchi
For 23: 46,92,713,805 (1656) Vicente
For 29: 493,580,1276 (2349) Vicente.
For 31: 372,496,1085 (1953) Vicente.


 
Spanish version : 1450 - Múltiplos con todos los dígitos

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