New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 8 Playing with Numbers self Practice 4C Solution
SOLUTION From Number 1 & 2:
SOLUTION From Number 3,4,5,6,7,8, & 9:
(10) Rumours: Rumours spread very fast. Sometimes an incident witnessed by just a few person becomes becomes the talk of the town within less than two hours. Suppose a man comes at about 8 a.m. to a town with a population of about 50,000 and conveys an interesting news to just three persons. This takes up say 15 minutes. Within 2 hours it becomes a talk of the town. Show, how is it possible.
SOLUTION Number 10:
(11) Number patterns
0 x 9 = 1
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
Investigate a similar number pattern where the first two line are:
1 x 8 = 9
12 x 8 + 2 = 98
SOLUTION Number 11:
(14) Blaise Pascal (1623 – 62) was a famous French mathematician and philosopher. One of his most important discoveries is known as Pascal’s Triangle. See if you can discover the secret of this pattern of numbers.
Solve.
(a) Write Row 8 of Pascal’s Triangle
(b) Write Row 9 of Pascal’s Triangle.
(c) Write Row 10 of Pascal’s Triangle.
(d) What is the sum of the numbers in Row 1 of Pascal’s Triangle?
(e) What is the sum of the numbers in Row 3 of Pascal’s Triangle?
(f) Find the sum of the numbers in Row 8 of Pascal’s Triangle without adding.
SOLUTION Number 14:
(15) Sudoku: Fill in the grid so that every horizontal row, every vertical column and every 3 x 3 box contains the digits 1 – 9, without repeating the numbers in the same row, column or box. You can’t change the digits already given in the grid.
9 | 3 | |||||||
7 | 5 | 8 | ||||||
9 | 2 | 4 | 1 | |||||
8 | 2 | 6 | ||||||
6 | 2 | 3 | 4 | |||||
3 | 5 | 7 | ||||||
2 | 6 | 5 | 8 | |||||
6 | 1 | 2 | ||||||
4 | 7 |
(16) One way of expressing 10 as a combination of five 9’s is 9 + 99/99 = 10. Find the further ways of doing so.
(17) A clock takes three seconds to strike 3 O’clock. How long does it take to strike 6 O’clock?
(18) What is the smallest integer that can be written with two digits?
(19) Write 1 by using all the ten digits.
(20) Write 10 with five 9s. Do it in at least two ways?
(21) Write 100 by using all the ten digits.
SOLUTION Number 15 to 21:
(22) Show four different ways of writting 100 with five identical digits.
(23) What is the biggest number that can be written with four 1s?
(24) Calculate the length of the strip of all the millimetre squares in one square metre, if placed one along side the other.
(25) Calculate the height of a pole made of all the milimetre cubes in one cubic metre, if places=d one atop another.
SOLUTION Number 22 to 25:
Please give solutions in proper hand writing
Please give answer in proper writting