find-the-sum-of-4-digit-even-numbers-formed-from-the-digit-1-2-3-4-

Question Number 36844 by tawa tawa last updated on 06/Jun/18

find the sum of 4 digit even numbers formed from the digit 1, 2, 3, 4

Answered by MJS last updated on 06/Jun/18

4 \times 4 \times 4 \times 2 = 128 even numbers

64 abc 2

64 abc 4

32 ab 1 c

32 ab 2 c

\dots

32 (1000 + 2000 + 3000 + 4000) = 320000

32 (100 + 200 + 300 + 400) = 32000

32 (10 + 20 + 30 + 40) = 3200

64 (2 + 4) = 384

sum = 355584

Commented by Rasheed.Sindhi last updated on 06/Jun/18

N i c e S i r!

Commented by tawa tawa last updated on 06/Jun/18

please what is 32 ab 1 c etc . from your solution . i can see that numbers that

end with 2 is 64, numbers that end with 4 is 64 . i {don}^{'} t understand the 32 ab 1 c etc

thanks . please explain

Commented by tawa tawa last updated on 06/Jun/18

And what if repetition of digit is not allowed

Commented by tawa tawa last updated on 06/Jun/18

God bless you sir

Commented by MJS last updated on 06/Jun/18

a b c stand for any combination of 1, 2, 3, 4

we have 128 numbers, each 32 start with

1000, 2000, 3000, 4000, each 32 contain

100, 200, 300, 400, each 32 contain 10, 20, 30, 40

if no repetition is allowed :

1234, 1324, 2134, 2314, 3124, 3214

1342, 1432, 3142, 3412, 4132, 4312

sum = 31116

Commented by tawa tawa last updated on 06/Jun/18

can we get that 31116 by calculation ? . i used your method above . am not

getting 31116 .

i appreciate your effort . God bless you sir

Commented by MJS last updated on 06/Jun/18

4 \times 1000 + 2 \times 2000 + 4 \times 3000 + 2 \times 4000 = 28000

4 \times 100 \times 2 \times 200 + 4 \times 300 + 2 \times 400 = 2800

4 \times 10 + 2 \times 20 + 4 \times 30 + 2 \times 40 = 280

6 \times 2 + 6 \times 4 = 36

28000 + 2800 + 280 + 36 = 31116

Commented by tawa tawa last updated on 06/Jun/18

wow great but i dont really understand . i want to understand so that i can know

it because of exam