What is the sum of all the four digit numbers formed using the digits 0, 1, 2 and 3. None of the two digits should be repeated.

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ROHAN

  • Mar 7th, 2006
 

starting with 1,2 & 3 series of no.

1230   2031  3012

1320   2013  3102       TOTAL SUM= 38664

1023   2103  3201

1032   2130  3021

1302   2310  3120

1203   2301  3210

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in addition to them
we have to add
0123
0321
0132
0213
0312
0231


these are also digits dude!!! so i think  your answer (38664) must be added with 1332
which leads to 39996 would be the right answer!!!  
what do u say guys??

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total number of such numbers = 18 

sum of all digits in units place :
0*2 ( 3 in thousands place)
1*2
2*2

0*2 (2 in thousands place)
1*2
3*2

0*2 (1 in thousands place)
2*2
3*2

------
24

4 in units place...2 carry

now tens place :
((1 +2) + (0 + 2) + (0 + 1)) + ((1+3) + (0+3) + (0 + 1)) + ((0+1) + (0+2) + (1+2)) 
----------------------------------      --------------------------------    -------------------------------
3 in thousands place                  2 in thousands place             1 in thousands place

=6 + 8  +6 = 20
20 + carry = 22

2 in tens place 2 carry

hundreds place :
this is similar to tens place
=20
20+ carry=22
2 in hundreds place...2 carry

thousands place :
6 combinations for each digit in thousands place (as 3! = 6)
6*3 + 6*2 + 6*1 =36
36 + carry = 38

therefore, sum = 38224

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