Flowers And Sparrows

Relevant wiki: Setting Up Equations

Let the number of flowers be $n$ . Then the number of birds is $n+1$ . When the birds were sitting in pairs, there was a flower left empty. Therefore,

$\begin{aligned} \frac {n+1}2 & =n-1 \\ n+ 1 &= 2n-2 \\ \implies n&= \boxed {3}\end{aligned}$

Total Number of Flowers=3

Let, sparrows are denoted by s and flowers are denoted by f then " Some sparrows came and each sat on a different flower, leaving one sparrow no flower to sit on" implies

s-1 = f

and sparrows sat in pairs on different flowers, this time leaving one flower without any sparrows implies

s/2 = f-1

and from later equation

s = 2f-2

placing in 1st equation

(2f-2)-1=f

2f-f-2-1=0

f-3=0 => f=3