BdMO National Primary 2016/6

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Primary 2016/6

Unread post by samiul_samin » Thu Feb 15, 2018 11:26 am

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?

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samiul_samin
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Re: BdMO National Primary 2016/6

Unread post by samiul_samin » Thu Feb 15, 2018 7:09 pm

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

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samiul_samin
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Re: BdMO National Primary 2016/6

Unread post by samiul_samin » Thu Feb 15, 2018 7:20 pm

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 $\fbox {11}$

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