Week 37

Example 1. Solve the number riddle:

Tell me who I am! Who I am!

Take away from me the number eight,

Divide further by a dozen to come up with

A full team for a game of cricket!

Example 2. Solve the teaser:

There was in the forest an old Peepal tree

The grand tree had branches ten and three

On each branch there lived birds fourteen

Sparrows brown, crows black and parrots green!

Twice as many as the parrots were the crows

And twice as many as the crows were the sparrows!

We wonder how many birds of each kind

Aren’t you going to help us find?

Solution 1. Let the required number be x.

The number is x.	x
Number eight	Means 8
Take away the number eight	Means −8
Take away from me the number eight	Means x − 8
Dozen	Means 12
Divide further by a dozen	Means (x – 8)  ÷ 12
To come up	Means =
A full team for a game of cricket	Means 11 (players)
Final form is	(x – 8)  ÷ 12 = 11
On transposition , ÷ changes to ×	(x – 8)  = 11 × 12
Calculation	x – 8  = 132
On transposition, – changes to ×	x = 132 + 8
Finally	x = 140

Therefore, required number is 140.

Solution 2. Ten and three branches means 10 + 3 = 13 branches and fourteen birds means 14 birds.

Given that, there are 13 branches and on each branch there lived 14 birds.

Total number of birds living in the tree = 13 × 14 = 182.

Three different birds are there, parrots, crows and sparrows.

Twice as many as the parrots were the crows means, the number of crows is double that of the parrots.

Twice as many as the crows were the sparrows means, the number of sparrows is double that of the crows.

Let the number of parrots be x.

The number of parrots is x.	Number of parrots is x.
Number of crows is double that of the parrots	So, number of crows is 2x
Number of sparrows is double that of the crows	So, number of sparrows is 2 × 2x = 4x
Total number of birds living in the tree	= 182
This means	x + 2x + 4x = 182
Simplification	7x = 182
On transposition , × changes to ÷	x = 182 ÷ 7
Finally	x = 26

Therefore, number of parrots = x = 26;

Number of crows = 2x = 2 × 26 = 52;

Number of parrots = 4x = 4 × 26 = 104.