When my grandfather died, he left his fine collection of coins, not more than 2500 of them, to his children, a different number to each of them, and in decreasing amounts according to their ages.

To the eldest of his children, he left one fifth of the coins, while the youngest inherited just one eleventh of them. Gaby, my mother (and third oldest of the children), received one tenth of the collection. All the other children received a prime number of coins.

How many coins did my aunt Isabel, second oldest in the family, inherit?

  • $\begingroup$ This puzzle is based on another puzzle in this site. I will reveal which once it is solved. $\endgroup$ – Bernardo Recamán Santos Apr 12 at 1:47
  • $\begingroup$ 1/130 chance you pick the right one! :):) $\endgroup$ – Voldemort's Wrath Apr 12 at 1:51
  • 2
    $\begingroup$ Does "All the other children received a prime number of coins" imply that all previously named children (eldest, youngest, Gaby) didn't get a prime number of coins? $\endgroup$ – bobble Apr 12 at 2:18
  • $\begingroup$ Those wanting to try a very similar question, can try this one $\endgroup$ – Hemant Agarwal Apr 13 at 12:55
  • $\begingroup$ @HemantAgarwal Which is indeed the fine puzzle on which I based mine. However, I have not been able to open link provided. $\endgroup$ – Bernardo Recamán Santos Apr 13 at 14:33

Aunt Isabel received

311 coins


The total number of coins has to be divisible by 5, 10, 11 and less than or equal to 2500. This leaves 22 posible totals (110, 220, 330, etc)
Isabel's total had to be a prime between 1/5 and 1/10th the total, and the remaining values have to be prime, between 1/10 and 1/11 in value and total to the right amount

After looking at the numbers

only the total of 2420 had enough primes between 1/10 (242) and 1/11 (220). The other totals minus 1/5, 1/10, 1/11 and all the primes between 1/10 and 1/11 were still larger than 1/5. With 2420 total, there are 6 primes, though we only need 5.

Therefore the totals are, by child's age

484 311 242 241 239 233 227 223 220, which add up to 2420. We didn't need the prime 229.
The solution is unique. No other total works and this is the only combination that gives a valid result.


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