Brain-Teaser 477: [Tribute of goats]
From The Sunday Times, 19th July 1970 [link]
His four wives have to make tribute of goats to the Khan of Bakristan. My job is to collect the goats.
“Kahn Sahib says each gift to be divisible by donor’s age which consists of first and third digits of her number of goats”, said Munshi. “I don’t know ages, but know the goats required from each”.
I knew their ages. To celebrate each wife’s 31st birthday the Khan had married a teenager, so I quickly jotted down the four numbers of goats — no names because Munshi was looking over my shoulder and reading each of my four numbers from right to left, as they do in Bakristan. “Numbers correct”, he said.
Having done things the opposite way my numbers agreed with his.
What are the ages of the 3rd and 4th wife?
This puzzle was originally published with no title.
[teaser477]
S2T2 
Jim Randell 3:05 pm on 2 May 2019 Permalink |
If we suppose the current ages of the four wives are:
Then the difference in the ages of consecutive wives is a number between 12 and 18.
And the numbers of goats must be:
(assuming each is a three digit number), where each number is divisible by the corresponding age.
And this set of numbers can also be read as:
This is enough to allow us to use the general alphametic solver [[
SubstitutedExpression()]] from the enigma.py library to find an answer.The following run file executes in 188ms.
Run: [ @replit ]
Solution: The third wife is 35. The fourth wife is 17.
When the first wife is 31, the new (second) wife was 13.
18 years later: The first wife is 49, the second wife is now 31, and the new (third) wife is 13.
18 years later: The first wife is 67, the second wife is 49, the third wife is now 31, and the new (fourth) wife is 13.
4 years later (brings us to now): The first wife is 71, the second wife is 53, the third wife is 35, and the fourth wife is 17.
The corresponding numbers of goats are: 781, 583, 385, 187 (1936 goats in total).
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