June 26, 2013

NUMBER PUZZLE 2

mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Here is another number puzzle. I'll tell you how to answer the first one then try to do the other by your own. Here is the first one:
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Let us try to decipher the pattern for the numbers.

In this number puzzle, try to focus on the results. For the first statement, if you notice, 1 is already the first digit and also the last digit. The middle digit, which is 2, comes from the sum of the two numbers.
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
For the case of 1 + 2, 1 is the leftmost digit but is not the rightmost digit. That means the pattern that we got in the first statement is not true to all the statements. 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
The only problem is how to make 2 to 4. We can multiply 2 by 2 and get 4 or square 2 to get 4. 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Let us apply that with the first statement. The square of 1 is 1. This is applicable to both statements now. 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Let us study the third statement. We cannot just copy the first number for the leftmost digit. They are not equal. 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
What is we square the first number? Let us check if all the digits are satisfied with the pattern that we got.
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Let us also see if it is applicable to the first and second statements.
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Yes, both statements are satisfied. How about the fourth statement?
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Now that all statements are satisfied, let us generalize the pattern for all the statements. Take note that the pattern would be:
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Now, let us apply the pattern to the last statement to find the missing number.
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Therefore, 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
It is now your turn to do same process. The following puzzle is similar to the one I presented above but there will be a slight difference. It's your turn to find the pattern. 
mathematics,IGCSE,patterns,symmetry,transformation,geometry,polygons,numbers
Goodluck! Hope you learned something from this... :)

Your comments ans suggestions are welcome here. You may write them in the comment box below. Thank you!

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