Name: Monika

Who is asking: Student
Level: Elementary

I need to place six numbers around a triangle, as such that one number is on each corner, and one number on each side making three numbers in one line, adding up to two hundred exactly. The number I have to use are, 40, 50, 60, 70, 80, 90. I have to use each one once, there for, each number cannot be repeated.

This was really hard for me, and this is why i ask for help.

Thank you,
A 4th grader

Hi Monika,

We have two answers for you, one from Claude and one from Chris.

From Claude

One of the difficulties is the 0 at the end. If you take it out, then the problem becomes to put the numbers 4, 5, 6, 7, 8, 9 as you say on the triangle, so that the numbers on a line add up to 20. But now, you have a clue: To get a sum of 20 with three numbers, you need either three even numbers, or two odd and an even.

In all you have three odd numbers: 5, 7, 9, and three even numbers: 4, 6, 8. Since 4 + 6 + 8 is 18, not 20, the three even numbers will not be on the same line, so each line will contain two odd numbers and an even number.

Do you see how this helps?

and from Chris

For one thing, you can simplify the problem by dropping the final zeros -- let the numbers be 4 through 9, and try for totals of 20 per edge. The next thing is to note that if you add together the numbers along each side you get 20 + 20 + 20 = 60. But you have added each corner number twice and each side number once, thus

20 + 20 + 20 = 60 = 2*(sum of corner numbers) + (other numbers).

It seems as if you'll need the corner numbers to add up to 21, and the others add up to 18.

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