## Brain-Teaser 195: Common frontier

**From The Sunday Times, 17th**** January 1965** [link]

The adjoining countries of Europhalia and Sopiculia have different standard units of weight and length, but both use the normal units of time. Although both countries use Arabic numerals, neither uses the denary (tens) method of counting, but each has a different integer less than ten as its counting base.

In reply to my request for more information a Europhalian friend wrote: “Our unit of weight is the Elbo, and there are 42 Elbos to 24 of their Solbos. The length of our common frontier is 21 Emils”. My Sopiculian correspondent replied: “16 Solbos weigh the same as 26 Elbos; the common frontier is 21 Somils long”.

I later discovered that in both countries there is a speed limit equivalent to our 50 mph. In Sopiculia this is defined by law as 104 Somils per hour.

What is the Europhalian speed limit?

This puzzle was included in the book **Sunday Times Brain Teasers** (1974, edited by Ronald Postill).

[teaser195]

## Jim Randell 9:02 am

on6 November 2022 Permalink |If the bases are E and S (both less than 10).

Then the ratio of the weights W = (Elbo/Solbo) is (according to to the two correspondents):

And we see from the digits used, E > 4 and S > 6, and S must be even, so:

We can then translate the correspondents statements into decimal to get:

And:

Solution:The Europhalian speed-limit would be expressed as: “134 Emils per hour”.LikeLike