Please help with a logical reasoning question, thank you

It may be wrong, but I only think of this

Suppose there are a total of ***x apples and one ***n people, where x and n are both positive integers

< p>The first person took: a(1)=5+0.2(x-5)

The second person took: a(2)=5+0.2(x-the first person The third person took: a(3)=5+0.2(x-5-first What one person took - what the second person took) = a(1)-0.2(1)-0.16a(1)=0.64a(1)

The nth person took 0.8^(n- 1) a(1) apples

The number of apples each person takes is a geometric sequence. The sum of n people is S=(a(1)-0.8^n a(1))/(1- 0.8)

=5a(1)-5*0.8^n a(1)

=2x-0.8^n (2x)

Just finished, it means that n people want to get the number x of apples, so

x=2x-0.8^n (2x)

So 0.8^n( 2x)=20

x=20*0.8^(-n)-20=5^(n+1)/4^(n-1)-20

The number of apples and the number of people are required to be positive integers

That is, 5^(n+1)/4^(n-1) is required to be an integer greater than 20. n can only be 1, and x can only be 5< /p>

There are only 5 pieces in a box and only 1 person