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The answer to most of these types of brain teasers is to know that the number is not limited to the number six, but caps the number of characters used (as in the equation will only show the numeral 6 six times).
The quickest way to solve the teaser is trial and error (perfectly reasonable math or scientific process in some instances.)
Numbers containing only 6's less than 144 are 66 and 6. Using the larger of the two numbers:
144-66 = 78 (four 6's left) --> 78-66 = 12 (two 6's left)
2*6 = 12 so a solution is 66+66+6+6 = 144
**The Mathematical and long way to prove the solution**
Since the problem makes clear that the addition operation is our only available math tool we can determine how many sixes we need to add together to get 144: 144/6 = 24. Numbers only showing 6 less than 144 are 66 and 6 which can also be written as 6*11 = 66 and 6*1 = 6.
Combining these mathematical statements provides the following equation:
6*24 = 6(x*11+y) --> 24 = 11*x + y
(where x and y are the number of 66's and 6's, respectively, in the equation we are building.)
We also know that 2*x+y = 6 (Two 6's in 66 for every x and one 6 in 6 for every y. The total 6's in the equation are limited to six.)
Solving the equations 11*x+y = 24 and 2*x+y = 6 using Gaussian Elimination:
11*x+1*y = 24
-(2*x+1*y) = -(6)
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9*x+0*y = 18 --> x = 18/9 = 2 (There are two 66's in the equation.)
2*2+y = 6 --> y = 6-4 = 2 (There are two 6's in the equation.)
It is proven that the final and only solution is 66+66+6+6 = 144
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Is 125x3 plus 144 a sum of cubes?
no
What is the sum of the first 144 decimal digits of pi?
Pi to 144 decimal places is written thus: 3.14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679 82148086513282306647093844609550582231725359 The sum of these first 144 decimal digits (after the decimal point) is 666.
Factors of 144 with a sum of 60?
36 and 24
If the sum of the digit is divisible by 3 the number is divisible by?
That means the number itself is divisible by three. the sum of the digits in 144, for example, is 9. 144 divided by 3 is 48. The sum of the digits in 21 is 3. 21 divided by 3 is 7.If the number is an even number and the sum of the digits is divisible by 3, the number is also divisible by 6. 144 is even and the sum of the digits is divisible by 3, so 144 is also divisible by 6. 144/6 = 24. And finally, if the sum is divisible by 9, the number itself is also divisible by 9. 27 is an example of this.
If the sum of 3 numbers is 144 what is the average of these three numbers?
48
Sum is 12 and 132?
The sum of 12 and 132 is 144
What does 36 pluss 144 equals?
The sum of 36 and 144 is 180.
What is the sum 3.6.8?
3.6.8 = 144
What is the sum of the angles in a decagon?
144
Factor 144 sum of 24?
18 and 6 16 and 8 12 and 12 three eights four sixes six fours eight threes twelve twos twenty-four ones
Factors of 144 with a sum of 51?
144/3 = 4848 + 3 = 51
Is 125x3 plus 144 a sum of cubes?
no
What is the sum of the first 144 decimal digits of pi?
Pi to 144 decimal places is written thus: 3.14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679 82148086513282306647093844609550582231725359 The sum of these first 144 decimal digits (after the decimal point) is 666.
What is the product of 144 and the sum of 24?
They could be: 12*12 = 144 and 12+12 = 24
What is the sum of all even factors of 60?
The sum is 144 if 60 is included, 84 if not.
Factors of 144 with a sum of 60?
36 and 24
If the sum of the digit is divisible by 3 the number is divisible by?
That means the number itself is divisible by three. the sum of the digits in 144, for example, is 9. 144 divided by 3 is 48. The sum of the digits in 21 is 3. 21 divided by 3 is 7.If the number is an even number and the sum of the digits is divisible by 3, the number is also divisible by 6. 144 is even and the sum of the digits is divisible by 3, so 144 is also divisible by 6. 144/6 = 24. And finally, if the sum is divisible by 9, the number itself is also divisible by 9. 27 is an example of this.
