Puzzles Questions

3+2×55=113

(or)

3+2×10=23

Let the 5 digit number be represented by abcde.

Then the 6 digit number, 1abcde x 3 = abcde1 (another 6 digit number)

Now let Y = abcde

Then (100000 + Y) x 3 = (Y x 10) + 1

300000 + 3Y = 10Y + 1

7Y = 299999

Y = 299999 ÷ 7 = 42857

The answer is letter ‘f’.

1 year = 12 months (February = 1 `f`, comes only once in the spelling of all the months)

1 month = 4 weeks (first, fourth = 2 f’s, comes twice in a month)

1 week = 7 days (first, fourth, fifth = 4 f`s, comes 4 times in a week)

1 day = 24 hours (four, five, fourteen, fifteen, twenty-four= 6 f’s, comes 6 times in a day

The logic in the challenge is

 81x6 = 9x6 = 54

144x7=84

Similarly, 64x8 = 8x8 = 64.

The logic in the given puzzle is 

4 + 4 = 4 * 4+1 = 4 * 5 = 20

5 + 5 = 5 * 5+1 = 5 * 6 = 30

6 + 6 = 6 * 6+1 = 6 * 7 = 42

7 + 7 = 7 * 7+1 = 7 * 8 = 56

Similarly

9 + 9 = 9 * 9+1 = 9 * 10 = 90.

Let the value to be find be 'x'.

 
Sum of individual column value = 14

 
C1 = 7 + 2 + 1 + 4 = 14
C2 = 3 + 8 + 1 + 2 = 14
C3 = 6 + 5 + 2 + 1 = 14

C4 = 2 + 4 + 4 + x = 14

x = 14 - 10

x = 4

Hence, the missing number is '4'.

From the hints,

Only two options for 1st and 2nd digits => 4,2 and 9,3 since it is single digits

Sum of second and third digit  = 10 

If 2 => 3rd digit = 8

If 3 => 3rd digit = 7

4th digit = 2nd digit + 1 => (2+1 =3) or (3+1 = 4)

Sum of all digits = 30

Let 5th digit be x

=> 1st possibility = 4 + 2 + 8 + 3 + x = 30 => x = 13 (Not possible since it has 2 digits)

=> 2nd possibility = 9 + 3 + 7 + 4 + x = 30 => x = 7

Therefore, the PIN is 93747