Question 27

The numbers $$1,4,7,10$$ and $$13$$ are placed in each box of the figure, such that the sums of the numbers in the horizontal or vertical boxes are the same. The largest possible value of the horizontal or vertical sum is ______.

Correct Answer: 24

Solution

To maximize the common sum, place the largest number $$13$$ in the centre because it is counted in both lines. The remaining numbers can be paired as $$1+10=11$$ and $$4+7=11$$. Thus each line has sum $$13+11=24$$.

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