Puzzle #207: Total recall
From New Scientist #3424, 4th February 2023 [link] [link]
I recently had the incredible opportunity of talking to an intergalactic traveller about her encounter with four extraterrestrial beings.
“The aliens have purple skin, long, floppy legs and large orange eyes”, she told me. “And they revealed to me the true nature of dark matter”.
I leaned in close with excitement.
“Unfortunately, I don’t remember anything about that. I do remember a great puzzle they told me, though. I asked them their ages, and they said that if you sum up the ages of only three of them, the possible totals are 24, 53, 54 and 61. From this, they told me that I could work out all four of their ages”.
Well, it isn’t exactly the secrets of the universe, but it will have to do. Can you work out the ages of the four aliens?
The presented partial sums are the total sum of all four ages each less a different one of the individual ages.
So if we add up all the partial sums we get 4× the total, less 1× the total, i.e. 3× the total. Hence:
And then the individual ages follow by subtracting each partial sum from this total.
Solution: The four ages are: 3, 10, 11, 40.