Student: A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die?
Options:
(A) 61
(B) 3
(C) 5
(D) 6
(E) 1.
Another student: Let's say, hmmm...
Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Final answer: (B).