A number theory problem by Anthony Ma-at
Number Theory
Level
1
There is a group of birds in a tree. If there are 2 birds in each cage the is one cage left. if there are 1 bird in each cage there will be 1 bird left.
Guess how many birds and how many cage is in the tree?
10 birds and 6 cages
4 birds and 3 cages
3 birds and 4 cages
20 cages and 11 birds
12 birds and 7 cages
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Let the number of cages be x. According to the first condition,no. of birds=2(x-1). Another condition,no. of birds =x+1. Since the no. of birds are same in both cases: 2(x-1)=x+1..... x=3 and hence the no. of birds =3+1=4.