BdMO National Primary 2016/6

[samiul_samin]

A number is called Tamata Number if it stays the same when the number is written in reverse order.For example, $121$ is a Tamata Number because,we get $121$, if $121$ is written in reverse order.Now what is the minimum G.C.D. (Greatest Common Divisor) of two four digit Tamata Number?

[samiul_samin]

Hint

In a 4 digit Tamata Number the fist and last digits are same.As well as, the second and third digits are same

Answer

11

[samiul_samin]

Solution

Suppose,$\overline{abcd}$ is a 4 digit Tamata Number.
So,$a=d;c=d$
$\overline{abcd}=1000a+100b+10c+d=1000a+100b+10b+a=1001a+110b=11(91a+10b)$
So, every 4 digit Tamata Number is a multiple of 11.
For this reason,we can say that the minimum G.C.D. of two 4 digit Tamata Number is $\fbox {11}$