Guessing game!

Define the following variables:

Rashed's month of birth is $m$ .

His day of birth is $d$ .

Value range of the variables:

$d∈(1;2;3; \cdots 31)$

$m∈(1;2;3; \cdots 12)$

Solving the problem:

Now we make use of the clues to find the exact value of the variables. The first clue tells us that $m$ and $d$ are cubic numbers. For better understanding,

$m=x^3$

$d=y^3$

Here, $x$ and $y$ are random variables and do not bear any significance in solving this problem.

Cubic numbers : $1=1^3$ , $8=2^3$ , $27=3^3$ , $64=4^3$ , $125=5^3$ and so on...

1 , 8 , 27 , 64 , 125

We limit the range of possibilities upto the 3rd term of this geometric sequence, as further terms exceed the value range. So, $m$ can be either 1 or 8. $d$ can be anyone of the three: 1, 8, 27.

The second clue tells us that the sum of $m$ and $d$ is $35$ . This gives us the equation: $m+d=35$ . Replace the variables with any of the values from the set of possibilities . Try picking randomly from the set of possibilities ​ and see which values fit into this equation.

Possible replacements:

$1+8\neq35$

$8+27=35$

We see that the first replacement is a wrong one as it does not meet the condition (m plus d must be equal to 35). However, the second replacement values fit perfectly into the equation and HURRAY! We have found out the values of the variables.

From this experiment, we can conclude that $8$ and $27$ are values of $m$ and $d$ , respectively.

Therefore, Rashed's birthdate is : $27$ / $08$ / $1996$ ( sequence D/M/Y )

The answer to be typed is : $\boxed{08271996}$

The date contains $d$ (for day) and $m$ (for month). The relation can be written as $d+m=35; d,m \in integer cubes$ If we take a look at the first few cube numbers, $1^3=1$ , $2^3=8$ , $3^3=27$ and $4^3=64$ , can see that $d + m = 35 < 4^3$ . Therefore $d,m \in (1;8;27)$ , which easily leads to $8+27=35$ . Because $m$ can be at most $12$ , it can only be 8 and 27 is left over for $d$ . The right solution is in the form $DDMM1996$ , which concludes to $\boxed{27081996}$