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Cracking of The Code in Steps...

**What was the challenge?**
Let's number the clues as **1**, **2**, **3**.
Now following step by step process here onward.
**1.** The numbers 3 & 1 are common in first & third combinations. Now both must not be the part of original number as in that case Clue 1 will be invalid.
**2.** If numbers 3 & 1 are not correct in third combination then the correct 2 numbers must be among** 5,7,9.**
**3.** But it can't be both 7 and 9 as again that would make clue 1 invalid! Hence, the 5 is part of the original key & in correct position as in third combination. So we have got **first** digit of key as a **5.**

**4.** The 1 correct number in clue 2 is 5 & that's in wrong position. If other is assumed to be 9 & to be in right position then it contradict the clue 3. So the **second **digit must be** 7.**

**5**.The only correct number in clue 1 is 7 & that's in wrong position. That means numbers **1,3,4,9** must not be the part of the code.
**6**. Since 3,4,9 eliminated in previous steps, the only number that is correct and in right position must be 6 in suggestion made by clue 2. So far we have got 3 digits of the code as **576XX.**
**7.** Last 2 digits can be any combination from 0,2,5,7,6,8. Now addition of all digits is equal to the number formed by last 2 digits. It's impossible that the addition of all digits exceeds 50. Hence, the **second last** digit must be **2.**
**8.** Now both** 57620 **or **57628** are perfectly valid where sum of all digits equals to number formed by last 2 digits.
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