Algebra Play | IT

Question 7

Use the same rule to fill these pyramids:

Question diagram 1
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Solution

In these number pyramids, each block's number is found by adding the numbers in the two blocks directly below it.

Step 1 — Fill Pyramid (i)

We need to find the number in the top block. This number is the sum of the two numbers below it.

6+26 + 2

=8= 8

8\boxed{8}

Diagram 1

Step 2 — Fill Pyramid (ii)

First, we find the numbers for the middle row. The left block in the middle row is the sum of 3 and 4.

3+43 + 4

=7= 7

The right block in the middle row is the sum of 4 and 3.

4+34 + 3

=7= 7

Now, we find the number for the top block. This number is the sum of the two numbers in the middle row (7 and 7).

7+77 + 7

=14= 14

14\boxed{14}

Diagram 2

Step 3 — Fill Pyramid (iii)

Let us start by filling the second row from the bottom. The first block is the sum of 5 and 4.

5+45 + 4

=9= 9

The second block is the sum of 4 and 5.

4+54 + 5

=9= 9

The third block is the sum of 5 and 0.

5+05 + 0

=5= 5

Now, we fill the third row from the bottom. The first block is the sum of the first two numbers in the second row (9 and 9).

9+99 + 9

=18= 18

The second block is the sum of the second and third numbers in the second row (9 and 5).

9+59 + 5

=14= 14

Finally, we find the number for the top block. This number is the sum of the two numbers in the third row (18 and 14).

18+1418 + 14

=32= 32

32\boxed{32}

Diagram 3

Answer

(i) The top number is 8. (ii) The numbers in the middle row are 7 and 7. The top number is 14. (iii) The numbers in the second row are 9, 9, and 5. The numbers in the third row are 18 and 14. The top number is 32.

More questions in IT

Q1

Context: Think of a number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of.

Q. I predict you get 2. Am I right? Try it out with different starting numbers. Do you always end up with the same value, 2? Why?

Q2

Context: Consider the following number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of. (This trick always results in 2).

Q. How would you change this game to make the final answer 3? What about 5?

Q3

Context: Consider the following number trick:

  1. Think of a number.
  2. Double it.
  3. Add four.
  4. Divide by two.
  5. Subtract the original number you thought of. (This trick always results in 2).

Q. Can you come up with more complicated steps that always lead to the same final value?

Q4

Context: In the date trick, the final answer is given by 100M+165+D100M + 165 + D, where MM is the month and DD is the day.

Q. Find the dates if the final answers are the following:

(i) 1269 (ii) 394 (iii) 296

Q5

Context: In the date trick, the final answer is given by 100M+165+D100M + 165 + D, where MM is the month and DD is the day.

Q. Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final answer, you might have to subtract some other number.

Q6

Try to devise your own 'Think of a Number' trick.

Q7

Use the same rule to fill these pyramids:

Q8

Fill the following pyramids:

Q9

What is the relationship between the numbers in the bottom row and the number at the top?

Let us start with the simplest pyramid.

Q10

What about a pyramid with three rows?

Using letter numbers for the bottom row, we can write an expression for the top row.

Q11

In the following grids, find the values of the shapes and fill in the empty squares:

Q12

Context: 6.5 The Largest Product

Q. Fill the digits 2, 3, and 5 in ×\square\square \times \square, using each digit once. What is the largest product possible?

Q13

Context: Mukta's trick: Choose a 2-digit number of different digits, reverse the digits to get another number, find their difference, and divide the result by 9.

Q. If we choose other 2-digit numbers, and follow the steps, will there always be no remainder?

Q14

Context: Suppose a two-digit number is abab. When it is reversed, the new number is baba. If b>ab > a, the difference is baab=9(ba)ba - ab = 9(b - a), which is divisible by 9.

Q. Can you work out what happens if a>ba > b?

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