[ Word Problems ]

Chuk and Gek were decorating the Christmas tree. To prevent them from fighting, their mother gave each of them the same number of branches and the same number of toys. Chuk tried to hang one toy on each branch, but he was short of one branch. Gek tried to hang two toys on each branch, but one branch remained empty. How many branches and how many toys do you think their mother allocated to the boys?

#
Try to do as Chuk did - hang one toy on each branch.

## Solution

Let's try to do as Chuk did - hang one toy on each branch, then one toy will be left over. Now, take two toys - one that is left over, and another one from one of the branches. If we now hang these toys as the second ones on the branches that still have toys from the first time, then on two branches there will be toys, and one branch will remain empty. If there were other branches besides these three, then on these "extra" branches there would be one toy each, which contradicts the condition. Thus, there were 3 branches, and there were 4 toys, respectively.