Page 86 - Ganit Kaushal

2. Find out the sum of the numbers in each of the following patterns (a) and (b) below. Don’t add them
one by one. Use mental maths to do it in a quicker way. (NCERT)

125 125 125
32 32 32 32 32 32 32 32
125 125
32 32 32 32 32 32 32 32 250
125 250 250 125
32 32 32 32 32 32 32 32 500
32 32 32 32 32 32 32 32 125 125
(a) (b) 250 500 1000 500 250
64 64 64 64
125 125
64 64 64 64 500
64 64 64 64 125 250 250 125
250
64 64 64 64 125 125
125 125 125

3. Find out the sum of the dots in the adjoining pattern. Don’t add them one by one.
Use mental maths to do it in a quicker way. (NCERT)

4. Write the Collatz sequences by taking their first term as:
(a) 12 (b) 17 (c) 28 (d) 39
5. Find the value of the expression {55 ÷ 5 × (18 – 7)} using the BODMAS rule.

6. Evaluate: 48 ÷ 3 × (9 + 3) – 56 ÷ 7 × (16 – 5) using the BODMAS rule.
7. Evaluate: 260 × [475 – {440 – (150 – 60 –50) + 20} – 50] using the BODMAS rule.
8. Evaluate: 38 – [18 – {20 – (16 – 4 ÷ 2 × 2)}] using the BODMAS rule.
9. Evaluate: 420 × 4 – 5 × 10 + 100 ÷ [12 × 5 – {10 + 8 × 30 ÷ (2 × 3)}] using the BODMAS rule.

3.14 GAMES AND WINNING STRATEGIES

Numbers can also be used to play games and develop winning strategies.
So, let’s play a very famous game called 21. Play it with your classmates. Then try it at home with your family
and make your own winning strategy.

Rules for the Game: There are two players, and they play the game by following the steps:
Step 1: The first player will say 1, 2 or 3.

Step 2: Then the two players take turns adding 1, 2, or 3 to the previous number.
Step 3: The player who reaches 21 first wins!

Play this game several times with your friends.
Are you able to plan your winning strategy?
Which player can always win if they play correctly?

What is the pattern of numbers that the winning player should say?
Well, I have played it several times, and I have made my winning strategy. I always try to reach 17 on
the second-last turn so that the other player has to say at least 18, and then I can reach 21 in my final
turn by adding 3 to it, and I will win. To achieve 17 on the second-last turn, I have to reach 13 on the
third-last turn.

84 Mathematics-6