If m is an integer positive, prove that the sequence {xn}n≥0 defined by the following rule is alternating with periodicity m.

xn = [2m | n] + [2m | m + n]

 

the topic is combinations and Induction

Find the least number of cuts required which can cut a cube into 60 identical pieces? 

How many small boxes of side 1 cm can be cut off from a cube of side 1 metre.

A cuboidal block of 6cm×9cm×12cm is cut up into an exact number of equal cubes. The least possible number of cubes will be

Three cuboids of dimensions 5cm×6cm×7cm,4cm×7cm×8cm and×2cm×3cm×13cm are melted and a cube is made. Find the edge of the cube.

Three rectangular solid metallic cuboids 20cm×10cm×5cm,12cm×10cm×4cm and 15cm×12cm×5cm are melted together and recast into solid cubes each of side 5cm. How many solid cubes can be made from the metal?

If 1=3

2=3

3=5

4=4

5=4

Then, 6=?

Which number is equivalent to 3^(4)÷3^(2)

This problem comes straight from a standardized test given in New York in 2014.

There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete? 

Add 8.563 and 4.8292.

Using only an addition, how do you add eight 8’s and get the number 1000