Logic Masters Deutschland e.V.

The 7 bridges (orange lines) of Koenigsberg, across the Pregel river (blue lines), became famous in 1736 when Euler proved it was impossible to cross the bridges only once each and return to the same point.

[Fiction] Not to be perturbed, the Koenigsberg council added a pedestrian only bridge (green line) and devised a walk across all 8 bridges with a start point (grey circle) and an end point (grey square). Some bridges limited the traffic one way with a barrier (X). You may determine the path and at least another with a different end point if you wish.

3 waterfalls (small blue rectangles) define 3 distinct river height regions. Stairs (small sandstone rectangles) join high and low land regions either side of the river. A flying fox (pink line) joins the highest point Tower (large diamond), across the river to the other side. A lift (small circle) goes from ground level to the top of the tower. Safety fences (grey lines) were built on the cliff edges. The river/land height for the whole river/land region is indicated in the region's large circles The 2 middle island land region heights are independent.

Rules:

Place the digits 1-9 into the grid without repeats in rows, columns or outlined irregular regions.

Start of the walk is an odd digit. End of the walk is an even digit. Adjacent digits to the lift are consecutive. Adjacent digits at the one way barriers sum to 10.

The sum of the digits along the river have an equal sum within each river region. Digits along the original bridges must differ by at least 4. Digits along the new pedestrian only bridge must differ by at least 5. The digits along the flying fox are a non-repeating consecutive set in any order. Digits along the safety fences are consecutive and in order.

Land regions are higher than any adjoining river regions. The river flows from the higher land regions down to the lower land regions. The river height drops across the waterfalls in the direction of the river flow. Bridges may join land regions of different heights.

Digits either side of the stairs are less than their land region's height unless they are the land region's height. The higher land region's stair digit is greater than the lower land region's stair digit.

Waterfall digits are not constrained by their region's river height. The higher river region's waterfall digit is greater than the lower river region's waterfall digit.

The Tower is higher than the two land regions that are joined by the flying fox.