A mathematical puzzle: a natural number divided by 10 more than two, divided by 11 more than three, divided by 12 more than four, divided by 13 more than five? You're wrong. Think again

A mathematical puzzle: a natural number divided by 10 more than two, divided by 11 more than three, divided by 12 more than four, divided by 13 more than five? You're wrong. Think again

According to the meaning of the question, we know that the natural number divided by 10, 11, 12 and 13 is less than 8 (the remainder can be divided by 8), so the natural number should be less than their common multiple by 8
[10,11,12,13]=4290
So the minimum natural number is 4290-8 = 4282

What's the minimum of a natural number divided by 11 plus 1 and 13 plus 3

n=11k1+1
n=13k2+3=11k2+2k2+3
11(k1-k2)-(2k2+2)=0
11(k1-k2)=2(k2+1)
k2+1=11
k2=10
n=133

A number less than 200, divided by 11 over 8, divided by 13 over 10, then what is the number?

This number can be divided by 11 and 13 after adding 3
The least common multiple of 11 and 13 is 11x13 = 143
So this number is
143-3=140