iNTELLIGENCE

IQ solution to: Beer Barrel and Ladder

The boundary points of the circle (barrel) with the floor and the wall are 0.6 m away from the edge. The distance from these boundary points to the boundary points of the ladder with the floor and the wall are x and y, respectively. x and y are concurrently the distances of the three boundary points of the ladder.

Therefore, we can write the following equation for the triangle:

(x + y)² = (x + 0.6)² + (y + 0.6)², or:
x × y = 0.6 × (x + y) + 0.36

In addition it is true that x + y = 5. From this follows that:

x × (5 - x) = 3.36, and the solutions are:

x₁ = 2.5 + 1.7 = 4.2 and x₂ = 2.5 - 1.7 = 0.8

The distances of the ladder-endings to the wall are 4.8 m and 1.4 m - and because of the “drunkenness” of the ladder, 4.8 m is naturally the solution.

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