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Table Total

Age 14 to 16 Short Challenge Level:
Using the rules in the table to find the total
As shown below, the first two numbers in the bottom row add up to 16, and the first two numbers in the right hand column also add up to 16, because of the addition rules of the table.

 

Now look at the 4 purple boxes in the diagram below. The sum of the top two numbers is equal to the number in the top right hand box, and the sum of the lower two numbers is equal to the number in the middle right hand box. So the sum of all 4 numbers is the same as the sum of the top and middle numbers in the right hand column - which is 16.

 

So now, as shown below, there are four areas of the table which contain numbers whose sum is 16.

   So the total is 16 + 16 + 16 + 16 = 64.

Notice that we didn't need to know anything about what was in any of the boxes except for the bottom right one.


Adding up all of the numbers and symbols in the table
Adding everything together gives
Total =  + 4 + ( + 4) + 8 +  + ( + 8) + ( + 8) + ( + 4) + 16.
Collecting like terms, Total = 3$\times$ + 3$\times$ + 52.

From the bottom row of the table (or you could use the last column), ( + 8) + ( + 4) = 16, so  +  + 12 = 16, so  +  = 4.

Then, multiplying by 3,
3$\times$(  + ) = 3 $\times$ 4, so
3$\times$ + 3$\times$ = 12.

So Total = 12 + 52 = 64.

You can find more short problems, arranged by curriculum topic, in our short problems collection.