Question

Find the smallest natural number which is 4 times smaller than the number written with the same digit but in the reverse order.

Answer 1

@Thoughts

Answer 2

Give me some time, please!

Answer 3

ok

Answer 4

Confused. @Zarkon @ganeshie8 @amistre64

Answer 5

[Sorry for tagging you mods but I think you all may help here. ]

Answer 6

reverse order would suggest at least a 2 digit number

Answer 7

if we let x equal 10 ....

(bx + a)/4 = ax + b

Answer 8

if there is not value for this, try it as an x^2 format

Answer 9

well ...

(10b + a)/4 = 10a + b :)

10b + a = 40a + 4b

6b = 41a

a/b = 6/41

Answer 10

6/39 that is ... forgot how to subtract "1"

Answer 11

reducing gets us 2/13 which suggest to me that this is perhaps a 3 digit number at best

Answer 12

The new number = 5 (the original one)

Answer 13

100c + 10b + a = 400a +40b + 4c

Answer 14

If we take :The new number = 4 * the original one

Then we have 3 times smaller not 4 times.

Answer 15

ok

Answer 16

So, if I am not wrong it should be :

The new number = 5 * the original number

Answer 17

Do you agree amistre?

Answer 18

4 times bigger than x is: 4x
4 times smaller than x is: x/4

not too sure how you are seeing this tho

Answer 19

ok ... ... ...

Answer 20

if we go with my original a:b setup; we have a 2:13 ratio such that

10(13) + 2 = 40(2) + 4(13)

132/4 = 10(2) + 13

132/4 = 33

which doesnt really fit since: a or b > 9 there isnt a nice reversal

Answer 21

Ok thanks @amistre64

Answer 22

multiples of 4 end in: 0,4,8,2,6

4n > 9 when n=3
4n > 99 when n = 25
4n > 999 when n = 250
4n > 9999 when n = 2500

at best, we want a number that starts and ends with a 2

Answer 23

not quite what i mean; the ends of the number are 2 and 4

2xxx4 and 4xxx2

Answer 24

hmm, make that 2 and 8; since 2/8 is about 1/4 and not 2/4

Answer 25

I

Answer 26

I tried a lot , amistre but there was no such number.

Answer 27

Awesome @amistre64 , it is 2718 * 4 = 8712

Answer 28

It was sure that the last and the unit digits must be 2 or 8.

So, 2..8 * 4 = 8..2

Using modulo further I got.

(The hundreds digit) mod 10 = 4(The tens digit) + 3

hmm, that means the hundreds digit is 1 and the tens digit has to be 2 or 7

So, the no. can be :

2128 or 2178

2128 * 4 = 8512 (So this is not true)

2178 * 4 = 8712 (its true now)

Answer 29

good job :)

Answer 30

Thanks a lot amistre.