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Hello all, it’s a new day and time for a new puzzle! First, the answer to yesterday’s logic puzzle Crossing the Desert:

tl;dr : the answer is 3.46 loads and yes it is possible to do this infinitely.

The official and technical answer from source:

“The following analysis of the desert-crossing problem appeared in the issue of Eureka, a publication of mathematics students at the University of Cambridge. Five hundred miles would be called a ‘unit’; gasoline sufficient to take the truck 500 miles will be called a ‘load’; and a ‘trip’ is a journey of the truck in either direction from one stopping point to the next.

Two loads will carry the truck a maximum distance of 1 and ⅓ units. This is done in four trips by first setting up a cache at a spot ⅓ unit from the start. The truck begins with a full load, goes to the cache, leaves ⅓ load, returns, picks up another full load, arrives at the cache and picks up the cache’s ⅓ load. It now has a full load, sufficient to take it the remaining distance to one unit.

Three loads will carry the truck 1 and ⅓ plus ⅕ units in a total of 9 trips. The first cache is ⅕ unit from the start. Three trips put 6/5 loads in the cache. The truck returns, picks up the remaining full load and arrives at the first cache with ⅘ load in its tank. This, together with the fuel in the cache, makes two full loads, sufficient to carry the truck the remaining 1 and ⅓ units, as explained in the preceding paragraph.

We are asked for the minimum amount of fuel required to take the truck 800 miles. Three loads will take it 766 and ⅔ miles (1 and ⅓ plus ⅕ units), so we need a third cache at a distance of 33 and ⅓ miles from the start. In five trips the truck can build up this cache so that when the truck reaches the cache at the end of the seventh trip, the combined fuel of truck and cache will be three loads. As we have seen, this is sufficient to take the truck the remaining distance of 766 and ⅔ miles. Seven trips are made between starting point and first cache, using 7/15 load of gasoline. The three loads of fuel that remain are sufficient for the rest of the way, so the total amount of gasoline consumed will be 3 and 7/15, or a little more than 3.46 loads. Sixteen trips are required.”

** Final note by Commius ** I myself got 4 loads but saw less than 4 might be possible but really couldn't get the maths right. So, congrats on anyone who came close!

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Now time for today’s puzzle which has a prize of 25 q7 tanks for the first person to message me with the correct answer and the supported detailed logic of the answer. Feel free to comment on the article and possibly offer answers though no prizes for comment section answers. Answers will be in tomorrow’s article.

White, Black and Brown

““Professor Merle White of the mathematics department, Professor Leslie Black of philosophy, and Jean Brown, a young stenographer who worked in the university’s office of admissions, were lunching together.”

“Isn’t it remarkable,” observed the lady, “that our last names are Black, Brown and White and that one of us has black hair, one brown hair and one white hair.”

“It is indeed,” replied the person with black hair, “and have you noticed that not one of us has hair that matches his or her name?”

“By golly, you’re right!” exclaimed Professor White.

If the lady’s hair isn’t brown, what is the color of Professor Black’s hair?””