Divided by 2 balance should be 1

January 24, 2014 by puzzler 2 Comments

Number Puzzle #70

Its a number.
Divided by 2 the balance should be 1,
by 3 bal 2,
by 4 bal 3,
by 5 bal 4,
by 6 bal 5,
by 7 bal 0,
by 8 bal 7.
Find the number? Understand it properly before answering.

Check your answer:-

Click here to See Solution

here balance means remainder

in order to solve we know that it should be a perfect multiple of 7 (As the remainder is 0). also we can see that it should end wither with 4 or 9 (since remainder is 4 when divided by 5), we can further remove 4 since remainder should be 1 when divided by 2 (it should be odd number).

now lets list multiples of 7 ending with 9

49 (7×7), 119(17×7), 189(27×7), 259(37×7)

49 is ruled out since remainder is 1 when divided by 8

if you see 119 it satisfied all the condition
119%8 -> 7
119%6 -> 5
119%4 -> 3
119%3 -> 2

Grand Father, Father and Grand Son

January 22, 2014 by puzzler 3 Comments

Number Puzzle #69

One Grand Father, One Father and One Grand Son.
Sum of their age is 140 Years.
Grand Son’s age in month is equal to Grand Father’s age in years.
Grand Son’s age in days is equal to Father’s age in weeks.
What is the Age of all three?
–In Hindi–
Ek Dada Ek Baap Ek Pota 3no Ki Total Age 140 Years Hai Pota jitne Month Ka Dada utne Saal ka Pota jinte din ka Baap utne week ka hai Batao 3no Kitne kinte Saal k Hain?

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Answer: Son’s age: 7 Years, Father Age: 49 Years and Grand Father’s Age: 84 Years.

Lets assume the age(in years) of Grand Father, Father and Son as GF, F and S respectively.
Sum of their age is 140 Years
=> Equation 1 => GF + F + S = 140
Grand Son’s age in month = Grand Father’s age in years
S*12 = GF => Equation 2=> GF = 12S
Grand Son’s age in days = Father’s age in weeks
S*365 = F*(365/7)
S = F/7 => Equation 3 => F = 7S

Now we have three variables and three equations, we can easily solve it
12S + 7S + S = 140
20s= 140 => S = 7
F = 7S = 49
GF = 12S = 84.

Number Puzzle #68, 1, 10, 30, ?, 130

January 16, 2014 by puzzler 5 Comments

Number Puzzle #68

missing number in 1, 10, 30, ??, 130

Check your answer:-

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Actually this is a GP with first element as 1 and variable factor. where the factor comes from this series
1, 3, 7, 13.

Tn = Tn-1 + 2^(n-1);
T1 = 1;
T2 = T1 + 2^(2-1)= 1 + 2 = 3;
T3 = T2 + 2^(3-1) = 3 + 4 = 7;
T4 = T3 + 2^(4-1) = 7 + 6 = 13

nth number in GP = first number * (10)(Tn-1 in series);
First Element in GP = 1;
Second Element in GP(i.e. n = 2) = 1*10*(T1 in series); = 10
Third element in GP(i.e. n =3) = 1*10*(T2 in series) = 1*10*3 = 30
Fourth element in GP (i.e. n =4) = 1*10*(T3 in series) = 1*10*7 = 70
Fifth element in GP (i.e. n =5) = 1*10*(T4 in series) = 1*10*13 = 130

Thus the missing number here is 70.

Number puzzle #67, 4+5+4+5=81

January 15, 2014 by Vipin 1 Comment

Number Puzzle #67

If
4+5+4+5=81
5+6+5+6=16
6+7+6+7=64
1+2+1+?=16
What is the missing number?

Click here to See Answer

First lets understand the pattern
4+5+4+5 => 18 => 1+8 => 9 => square of 9 => 81
5+6+5+6 => 22 => 2+2 => 4 => square of 4 => 16
6+7+6+7 => 26 => 2+6 => 8 => square of 8 => 64

Thus the patter is sum of the digits till we get single digit and then square of the the single digit.

Method 1:
So lets assume the missing number is x

thus 1+2+1+x = x + 4
Now if x is less then or equal to 5(i.e. x+4 is single digit)
(x+4)(x+4) = 16 => x = 0

Now if x is greater then 5( i.e. x + 4 is two digit number)
lets replace x by 6+y (where y is single digit)

x+4 => 6+y+4 => 10 + y => y +1 => (y+1)*(y+1) = 16 => y = 3

thus x = 6+y = 9.

Note: If we assume missing number can be more then single digit.

Method 2:

its the reverse engineering method => to get 16 the sum of digits should be 4

we already have 1+2+1 = 4 thus missing number can be 0
other ways to get the sum of digits as 4 => 13, i.e. missing number = 13-4 = 9
other ways is 22, i.e. missing number 22-4 = 18
other way is 31, i.e. missing number 31 – 4 = 27
other way is 40, thus missing number 40 -4 = 36

so there can be more such numbers

Seven thieves and diamonds

January 12, 2014 by puzzler 7 Comments

There are seven thieves, They steal diamonds from a diamond merchant and run away in jungle. While running, night sets in and they decide to rest in the jungle When everybody’s sleeping, two of the best friends get up and decide to distribute the diamonds among themselves and run away. So they start distributing but find that one diamond was extra. So they decide to wake up 3rd one and divide the diamonds again …..only to their surprise they still find one diamond extra. So they decide to wake up fourth one. Again one diamond is spare. 5th woken up……still one extra. 6th still one extra. Now they wake up 7th and diamonds are distributed equally.

How many minimum diamonds they steal?

Check your answer:-

See Solution

Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
x = 1 + N1*2;
x = 1 + N2*3;
x = 1 + N3*4;
x = 1 + N4*5;
x = 1 + N5*6;
x = N6*7;
where N1, N2, N3, N4 and N5 are integers.
From above we can also say
N1*2 = N2*3 = N3*4= N4*5 = N5*6 = y

Now y should be divisible by 2, 3, 4, 5 and 6, its nothing but common multiple of all.

LCM of 2, 3, 2*2, 5, 2*3 => 2*3*2*5 => 60

at the same time common multiple + 1 should be divisible by 7 as well.

60 + 1 is not divisible by 7
120(60*2) + 1 is not divisible by 7
180(60*3) + 1 is not divisible by 7
240(60*4) + 1 is not divisible by 7
300(60*5) + 1 is divisible by 7

Thus they must have stolen minimum 301 diamonds.

Product of 5 different temperatures

January 6, 2014 by puzzler Leave a Comment

Number Puzzle #66
The product of 5 different temperatures is 12. If all of them are integers then find all the temperatures.

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product of 5 different integers is 12.

Lets consider first product of first 3 smallest integers
1*2*3 = 6
Now if we take the next smallest intege i.e. 4 then the product will become 24 thus we need to go back and consider negative numbers

thus (-2)*(-1)*1*2*3 = 12.

How many toffee’s you can get in Rs.15

January 4, 2014 by puzzler Leave a Comment

Number Puzzle #65
Cost of one toffee is Rs.1 and as a special promotion scheme you get 1 toffee free for three wrappers.
How many toffee’s you can get in Rs.15?

–In Hindi– 1 rs ki ek toffee. 3 wrappers k sath ek aur toffee milti hai.. u’v got Rs.15.. how many total toffee’s u get?

Check your answer:-

Click here to See Answer

First of all you get 15 toffee in Rs.15, then you get 15/3 = 5 toffees from 15 wrappers.

Now you have 5 wrappers => 1 toffee + 2 wrappers => 3 wrappers => 1 toffee
Total number of toffees you get => 15 + 5 + 1 + 1 => 22 toffee’s.

Next number in the series 1, 11, 21, 1211

January 4, 2014 by puzzler Leave a Comment

Number Puzzle #64

What will be the next number in the series?

Next number in series 1, 11, 21, 1211, 111221

Check your answer:-

Hint: If you really need

Next number is : 312211, Now can you guess the next number?
Check your answer:-

See Answer with Explanation

Here we need to count the number of individual digits, how many 1’s, how many 2’s etc.
for example
1 => one 1 => 11
11 => two 1 => 21
21 => one 2 one 1 => 1211
Thus to get 5th number in the series
111221 => three 1 two 2 one 1 => 312211
And to get the sixth number in the series
312211 => one 3 one 1 two 2 two 1=> 13112221

If 11 + 11 = 8, 12 + 12 = 12

January 2, 2014 by puzzler 7 Comments

Number Puzzle # 63

If 11 + 11 = 8, 12 + 12 = 12, 13 + 13 = 16 14 + 14 = 16 Then 16 + 16 = ?

If
11 + 11 = 8,
12 + 12 = 12,
13 + 13 = 16
14 + 14 = 20
Then
16 + 16 = ?

Check your answer:-

See Explanation

Answer is 28
How?
Right side number is equal to the sum of the digits on left side multiplied by 2
for ex.
11 + 11 => (1+1+1+1)*2
Thus
16 + 16 => (1+6+1+6)*2 = 28.

10,20,74,100 what will be the next number

December 30, 2013 by puzzler Leave a Comment

Number Puzzle #62

10,20,74,100. What will be the next number in the series?

next number 10, 20, 74, 100, ?

Check your answer:-

Click here to See Solution

The Next number in the series is 202.

Explanation:-
Natural number starts with 1,2,3,4,5,6……….
This series is derived by adding 2 consecutive odd Natural Numbers and even natural numbers

first 2 odd natural numbers are 1 and 3 = i.e. square of 1 + square of 3 = gives 10 ( first number)
first 2 even natural numbers are 2 and 4 = Square of 2 + square of 4 = gives 20 ( second number)
second 2 odd natural numbers are 5 and 7 = gives 74 (third number)
second 2 even natural numbers are 6 and 8 = gives 100 ( fourth number)
third 2 odd natural numbers are 9 and 11 which gives 202 ( 5 th number)

Answered by : Vishal Vinchankar

Number Puzzle #70

Number Puzzle #69

Number Puzzle #64

Number Puzzle # 63

Number Puzzle #62

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