Question

A flock of pigeons flew to a tall tree. Some of them perched on the branches, others landed under the tree. The pigeons sitting on the branches called to those under the tree, “if one of you joins us, there will be twice as many of us than you.” Then, those under the tree answered, “It’s true, but if one of you joins us, there will be as many of us as of you. Please help.

Answer 1

There are 7 on the tree, and 5 below

Explanation:

If one left the bottom, there would be 8 on top and 4 below. Therefore, twice as many. If one left the top it would be both 6 and 6.

Answer 2

• 7 pigeons sitting on the branches, 5 pigeons under the tree

Explanation:

• Number of pigeons on the branches = b
• Number of pigeons under the tree = t

We got equations below:

• b + 1 = 2(t - 1) ⇒ b = 2t - 3
• b - 1 = t + 1 ⇒ b = t + 2

Eliminate b and solve for t:

• 2t - 3 = t + 2
• 2t - t = 2 + 3
• t = 5

Then find b:

• b = t + 2 = 5 + 2 = 7