The orange thief

The orange thief

A thief, a basket of oranges from the market robbed and escaped among the orchards. When jumping a fence, the middle half lost. Persecuted by a dog, half less half abandoned. He tripped on a rope and the middle half scattered. In his den, two dozen kept. You who seek wisdom, tell us,

How many oranges did the thief steal?


This is one of the problems that are solved from back to front. We start from the 24 oranges that he kept in his lair.

"Loses the middle half to jump the rope," then at that time had double + 1 oranges, that is: 24 × 2 + 1 = 49.

“Persecuted by a dog, the least half half lost”, therefore, at that time, it had double - 1 orange, that is: 49 × 2 - 1 = 97.

"The middle half lost when the fence jumped", therefore it had double + 1 oranges, that is: 97 × 2 + 1 = 195.

The thief stole 195 oranges.