Cracking with spy

Number Theory Level 2

A $\text{spy}$ must be crack a computer code. Spy know that code has exactly $\text{10 digit}$ and spy exactly cracked $\text{ 9 digit}$ of code. The code can like below:

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{?}~}$

But now :

can spy crack the last digit with at least 11 entring?

$\text{Note: the last digit must be a non-negative integer . }$

Not enough information No Yes May be

1 solution

Matin Naseri
Feb 8, 2018

The all possible integer for last digit are $\text{(0,1,2,3,4,5,6,7,8,9)}$

The all possible code are like below :

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{0}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{1}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{2}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{3}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{4}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{5}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{6}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{7}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{8}~}$

$\boxed{~{7}~{9}~{0}~{1}~{3}~{5}~{4}~{3}~{2}~{9}~}$

The total possible code is $\text{10 possible }$ .

Thus we can crack code with $\text{11}$

Cracking with spy

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