1. By similar triangles, h/3 = x/(x+y)
Similarly, h/6 = y/(x+y)
Adding, h/3 + h/6 = 1 (etc.)
2. Similarly, 2.5/k + 2.5/6 = 1 (etc.)
where k is height of shorter pole.
3. x/12 = 2.5/k (etc.)
THIS MONTH'S QUIZ
Tommy wrote down three 3-digit numbers; the second number was twice the first, and the third was three times the first. To his surprise he discovered that altogether he had then written each of the digits 1 to 9 once only.
Find all possible values for Tommy's first number.