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Mathematical Puzzle

Guess the pincode

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A person forgot his 5 digit pin code, but he remembers some hints.

  1. 1st digit is square of 2nd digit.
  2. Sum of 2nd and 3rd digit makes 10.
  3. 4th digit is 2nd digit+1.
  4. Sum of 5th and 3rd digit makes 14.
  5. Sum of all 5 digits = 30

Can you guess the person’s pin code from above hints ?


See Answer
Pin code is 93747.
How?
Lets assume second digit is x, then first digit should be x^2 and fourth digit should be x+1.

also assume, 3rd digit is y then 5th digit should be 14-y.
So the number will look like this:-
<x^2><x><y><x+1><14-y>

As we also know the sum of all digits, we can say

x^2 + 2x +1 +14 = 30
(x+1)^2 = 16
x+1 = 4
x = 3

As sum of 2nd and third digit is 10 => x+y = 10 => y=7
Thus the pin code is 93747.

How many games to determine a champion?

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There are 97 baseball team participating in a tournament. The champion is chosen by the usual elimination scheme. That is, all teams are divided into pairs, and two teams of each pair play against each other. The loser of each pair is eliminated, and the remaining teams are paired up again.
How many games must be played to determine a champion?
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0.999… = 1 #55

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0.9999999…….. = 1, true or false?

0.999.... = 1, Right or Wrong?

0.999…. = 1, Right or Wrong?


See Answer

Its Right, yes 0.999 followed by infinite 9’s is equal to 1.

Proof 1 for 0.999… = 1

x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

Proof 2 for 0.999… = 1

1/3 = 0.333...
3x(1/3) = 3x(0.333...) = 0.999...
1 = 0.999...

Get number 28 # 53

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How you can get number 28 by using following numbers and operators

Numbers: 1, 5, 7 and 8.
Operators: +, -, * and /
You can use ( ) brackets as well.

Rules:-

  1. You can use each number only once.
  2. You can not use 1 and 5 as 15.
  3. You have to use all of the above number mentioned (1,5,7 and 8)


See Answer

There are multiple solutions
Solution 1: (8-5+1)*7 = 28
Solution 2: 7*5 – 8 + 1 = 28

10 digit number #52

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Find the 10 digit number satisfying below conditions

Its first digit is the number of occurrence of 0’s in the number.
Second digit is the number of occurrence of 1’s in the number.
Third digit is the number of occurrence of 2’s in the number.
4th digit is the number of occurrence of 3’s in the number.
and so on up to 10th digit(which is number of occurrence of 9’s in the number).

See Answer

Only 10 digit number satisfying these conditions is 6210001000.

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