4.1 For Eeyore's Birthday, Winnie-the-Pooh, Owl, and Piglet decided to give balloons. Winnie-the-Pooh prepared twice as many balloons as Piglet, and Owl prepared three times as many balloons as Piglet. When Piglet was carrying his balloons, he was in a hurry, stumbled, and some of the balloons burst. Eeyore received a total of 31 balloons for his party. How many balloons did Piglet end up giving?
# Answer: 1

Solution. If Piglet hadn't burst his balloons, then Eeyore would have received exactly 6 times more balloons than Piglet prepared. The next number after 31 that is a multiple of 6 is $36, 36: 6=6$, which means Piglet prepared no less than 6 balloons.

If all of Piglet's balloons had burst, then Eeyore would have received exactly 5 times more than Piglet prepared. If Piglet initially had 7 or more balloons, then even now Eeyore would have received at least 35 balloons, which is not the case. Therefore, Piglet prepared exactly 6 balloons. If everything had been fine, Eeyore would have received 36 balloons, but since 5 burst, Piglet gave 1 balloon.