What 5-digit number when multiplied by 4 gives you its reverse?

Question

For example, ABCDE x 4= EDCBA, what is the value of each digit (all are of different value).Thank you!

Answer 1

First, A must not be greater than 2, becaue then 4*ABCDE will have 6 digits, and it cannot be 1 becaue it is the unit digit of EDCBA.

Now E must be 8.

B must be odd, so BA can be divisible by 4, it should be 1 so AB * 4 will not exceed 90. (23 * 4) = 92

21CD8 * 4= 8DC12

8*4 = 32, therefor 4D must end with 8. D can only be 2 or 7.

21C28 * 4 = 82C12

Impossible because 21*4 = 84, so D = 7

21C78 * 4 = 87C12.
Now, because the sum of digits hasen't changed by multiplying the number by 4, ABCDE must be divisible by 9.
So c must be either 0 or 9

78 * 4 = 312, so it's impossible that C is zero, how about 9?
Yes, it works!!!
ABCDE = 21978

Answer 2

A=2
B=1
C=9
D=7
E=8

Answer 3

well a number is just an equation with powers of 10 so the number 1 is actually 1 * 10^0 the number 23 is actually 2 * 10^1 + 3 ^10^0 so your 4 digit number is simply abcd now you know the number when times 4 is 4*abcd = bcda this is what you want this means you have to have certain values for a because 4*8 will be 32 which means it will be 5 digit number at the end for example 4000 * 4 = 16000 thats 5 digit ending so it cant be the answer so when you have 1000a + 100b + 10 c + d thats the number you start with and times by 4 4*(1000a + 100b + 10c + d) = 4000a + 400b + 40c +4d) we want this to equal the reverse of the digits the reverse of a b c d is d c b a when we times by the values of 10 each represent thats d*1000 + c*100 + b*10 + a *1 these you want to be equal so 4000a + 400b + 40c +4d = 1000d + 100c + 10b + a then just subtract the one from the other 4000a - a + 400 b - 10b + 40 c - 100c + 4 d- 1000d = 0 3999a + 390b - 60 c - 996d = 0 and solve for the values does that help you with what they mean they pick a = 2 and d = 8 because abcd * 4 = dcba so a*4 = d the only values you can have are 1*4 = 4 or 2*4 = 8 3*4 = 12 wont work because it makes the number 5 digits after its multiplied by 4

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Answer 4

1

Answer 5

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Answer 8

divide 4 by 9
that would give you 0.44444444444444444.........
that means 4 =(10-1)0.4444...........
4=4.444444444444.........-0.4444444444......
therefore 4=4
hence proved


how's that!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 9

you should solve

40000A + 4000B + 400C + 40D + 4E =
10000E + 1000D + 100C + 10B + A
--------------------------------------------------------

30000A + 3000B + 300C + 30D + 3E = 0

or same

10000A + 1000B + 100C + 10D + 1E = 0

with a,b,c,d,e digits positive, there is no solution

so the answer is : there is no such number .
except for 00000

hmmm i made a minor mistake ....

Answer 10

21978