## Brain-Teaser 454

**From The Sunday Times, 25th January 1970** [link]

The card of the course at Triangle Park Golf Club gives the total length of the first 9 holes as 3,360 yards. Par for the individual holes (numbers 1 to 9 respectively) being 5, 4, 5, 4, 3, 4, 4, 3, 5 (total 37).

Closer inspection of the card would show that the lengths of the holes (each a whole number of yards) are such that holes 1, 2 and 3 could each form a different side of the same right-angled triangle (Triangle A) and that other right-angled triangles could similarly be formed from lengths equal to those of holes 4, 5 and 6 (Triangle B); 7, 8 and 9 (Triangle C); 1, 4 and 7 (Triangle X); 2, 5 and 8 (Triangle Y) and 3, 6 and 9 (Triangle Z).

Moreover, the total length of the three holes forming Triangle A, the total length of the three holes forming Triangle B, and the total length of the three holes forming Triangle C could similarly form the three sides of another right-angled triangle (Triangle ABC) while yet another right-angled triangle could similarly be constructed from the total lengths of the holes forming triangles X, Y and Z (Triangle XYZ).

In triangle ABC the sides would be in the ratio 5:3:4.

The length of each of the par 3 holes is between 150 and 250 yards (one being 168 yards); the par 4 holes are between 250 and 450 yards; and the par 5 holes are between 475 and 600 yards (one being 476 yards).

What are the lengths of holes 2, 6 and 7?

[teaser454]

## Jim Randell 10:33 pm

on21 February 2019 Permalink |This Python program uses the [[

`pythoagorean_triples()`

]] function from theenigma.pylibrary to find appropriate triangles. (Originally written forTeaser 2910).Run:[ @repl.it ]Solution:Hole 2 is 280 yards. Hole 6 is 357 yards. Hole 7 is 420 yards.There is only one solution:

In fact if the triangle constraints for A, B, C, X, Y, Z, ABC, XYZ are satisfied, there is only a single solution even if the conditions for the total distance, ratios for ABC, and the specific distances for par 3 and 5 are ignored (lines 38, 47, 50).

LikeLike

## Jim Randell 9:53 am

on23 February 2019 Permalink |This puzzle is a good candidate for solving with a declarative set of constraints.

Here is a

MiniZincmodel, that solves the puzzle in 93ms.LikeLike

## GeoffR 11:07 am

on23 February 2019 Permalink |LikeLike