Question

A keypad lock on a door has a code of five different digits. can you solve and find the digits by using the six clues given below
1) there are no zeros in the five digit code
2)the first digit is smaller than the second digit
3) exactly two of five digits are odd
4) the middle digit is perfect square
5) the two digit number formed by the fourth and fifth digits is a perfect square.
6) the two digit number formed by third and fourth digit equal to the first digit multiplied by the second digit​

Answer 1

The answer is 67425

Step by step explanation:

There are no zeroes in the code.

The middle digit is a perfect square . It can be 4 or 9. But 9 will not come due to condition 6.

First digit × second digit = 2 digit number by 3rd and 4th digit. As we already know the 3rd digit is 4 so it is possible when the 4th digit is 2 . So the number becomes 42 and the first 2 numbers 6 and 7. As first digit is smaller than 2nd one so 6 is first number and 7 is second.

( Hint : to try crack the code yourself write down all the possible perfect squares with uni digit numbers and start. When you know the mid no. is 4 then trying out the combinations from the written square numbers, only 25 is possible as all the other combinations are a product of 2 digit and one digit number or else prime numbers. Whereas when the number is 25 the number 42 is a product of 6 and 7.)

According to condition 5 when 4th digit is 2 then to make it a perfect square the fifth has to be 5.

Two numbers are odd - 7 and 5 are odd.

Thus the code is 67425.

Thank u.

Hope this helps you.

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@spyder