Onmatu- General Math Learning Article

Amazing simple Math problems II


         We will start again like in the first part with a simple problem: we draw a circle and we split that circle in 10 equal regions, then we make the horizontal diameter more thick so that is more clear which one is the upper half and which one is the lower half, then we put each digit from 0 to 9, so in total 10 digits, in each section of the circle like in the image below:

                                                            

          Your task is to answer the following question:

          How can you arrange the digits so that if you add the digits in the upper half and the digits in the lower half you get consecutive numbers? (Example: 7+1+8+9+4=29, 3+2+0+6+5=16, so the numbers 16, 29 are not consecutive, you need to arrange the digits so that you get consecutive numbers) 
          --> Consecutive numbers means numbers that follow each other in order and they have a difference of 1 between every two numbers.

          We will start again with a simple problem: we draw a circle and this time we split that circle in 9 equal regions like in the image below: 

                                                           

           Then we split that circle again in 3 equal parts like in the image below, look at the grey color sides:  

                                                           

           Now we have the digits from 1 to 9 so in total 9 digits. We can put each digit in each section of the circle like this:  

                                                            

          This is just an example of how digits are arranged in the sections of the circle and the condition is that the digits can't be repeated so the rule is: each section of the circle has a different digit from those 9. Your task is to answer the following questions:

          a) How can you arrange the digits so that if you add the digits which are placed in each of those 3 grey sections will give you the same sum? (Example: 1+2+7=10, 6+4+8=18, 9+3+5=17 so the sums are not equal, you need to arrange the digits so that you get equal sums)
          b) a) How can you arrange the digits so that if you add the digits which are placed in each of those 3 grey sections will give you consecutive numbers? (Example: 1+2+7=10, 6+4+8=18, 9+3+5=17 so the numbers 10, 18, 17 are not consecutive, you need to arrange the digits so that you get consecutive numbers) 
          c) How can you arrange the digits so that if you multiply the digits which are placed in each of those 3 grey sections will give you the same product? (Example: 1*2*7=14, 6*4*8=192, 9*3*5=135 so the products are not equal, you need to arrange the digits so that you get equal products)

          Thank you for your time
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