Number Puzzle #181
If
2×3=15
2×5=20
2×7=30
2×11=?
Very Difficult
Difficulty Level – Very Difficult
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İf 1*36=36, 8*23=23 Then 9*10=?
If 1*36=36
8*23=23
8*67=1
Then
9*10=?
Number puzzle #67, 4+5+4+5=81
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?
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
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
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