## Teaser 2877: Four steadings and a numeral

**From The Sunday Times, 12th November 2017** [link]

Farmers Al, Bo, Cy and Di have different double-digit numbers of sheep kept in their respective steadings. Al has the fewest and his number of sheep is a certain fraction of Bo’s number of sheep. Also, Bo’s number of sheep is that same fraction of Cy’s number, and Cy’s number is that same fraction of Di’s.

If I told you the total of Bo’s number of sheep added to Cy’s, then you would be unable to work out all their numbers of sheep. Similarly, if instead I told you just Bo’s number of sheep, then you would be unable to work out all the other numbers.

What (in the order Al, Bo, Cy, Di) are their numbers of sheep?

[teaser2877]

## Jim Randell 10:31 am

on31 March 2020 Permalink |This Python program looks for possible geometric sequences for

A, B, C, D(the numbers of sheep). And then uses the [[`filter_unique()`

]] function from theenigma.pylibrary to find sets where(B + C)does not identify a single sequence, and whereBdoes not identify a single sequence. The solution is in the intersection of these two sets.This Python program runs in 62ms.

Run:[ @repl.it ]Solution:The numbers of sheep are: Al=16, Bo=24, Cy=36, Di=54.Each term in the 3/2 times the previous term.

There are 6 possible geometric sequences:

[1], [4] have the same value for B + C (= 60).

[3], [4] have the same value for B (=24), and [5], [6] have the same value for B (= 36).

The solution occurs in both sets, so is sequence [4].

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## GeoffR 5:06 pm

on1 April 2020 Permalink |The following programme gives the same six sequences for A,B,C and D.

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