What’s in a Name?

Given: Deba and Deep used tally marks on the wall to count their cows. When they returned, they struck out one mark for each cow that entered. Two marks were still left, but no cows were seen outside.

Why were Deba and Deep worried?
Deba and Deep were worried because 2 tally marks were still left on the wall even after all the cows they could see had entered. This meant that 2 cows had NOT come back home — they were missing.

How many cows had reached home?
If the total number of marks on the wall was, say, $N$, and 2 marks were left un-struck, then the number of cows that reached home $= N - 2$.

*(Since the exact number of marks in the image cannot be seen, the answer follows the pattern: Total cows − 2 = cows that reached home. Two cows were missing.)*

Final Answer: Deba and Deep were worried because 2 cows were missing. The number of cows that reached home was 2 less than the total number of cows they had started with.

Given: Hemant has 36 cows and 23 sheep.

Concept: We use tally marks to count. We draw 4 vertical lines and then cross them with a diagonal line to make a group of 5. This makes counting easier.

Tally marks for 36 cows:
We make groups of 5:
$$36 = 5+5+5+5+5+5+6$$
That is 7 groups of 5 and 1 group of 1 — actually:
$$36 = 7 \times 5 + 1$$
So we draw 7 complete tally groups (each group = $\cancel{||||}$) and 1 extra mark.

Tally marks for 23 sheep:
$$23 = 4 \times 5 + 3$$
So we draw 4 complete tally groups and 3 extra marks.

Final Answer:
- Cows (36): $\cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ |$ (7 groups of 5 and 1 extra)
- Sheep (23): $\cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ |||$ (4 groups of 5 and 3 extra)

Given: A group of animals and birds. We need to find the one with the most letters (longest name) and the one with the fewest letters (shortest name).

Concept: Count the number of letters in each animal/bird name and compare.

*(Note: The exact list of animals shown in the image is not visible. The method below applies to any list. A typical set used in this exercise includes animals like: Elephant, Cat, Butterfly, Hen, Crocodile, Bee, etc.)*

Method — count letters in each name:

| Animal | Number of Letters |
|---|---|
| Elephant | 8 |
| Butterfly | 9 |
| Crocodile | 9 |
| Cat | 3 |
| Hen | 3 |
| Bee | 3 |

First Team Captain (Longest Name): Butterfly or Crocodile — 9 letters

Second Team Captain (Shortest Name): Cat / Hen / Bee — 3 letters

Do you know any animal with a longer name?
Yes! For example, Hippopotamus has 12 letters, which is longer than 9 letters.

Final Answer:
- First team captain: The animal with the most letters in its name (e.g., Butterfly/Crocodile — 9 letters).
- Second team captain: The animal with the fewest letters in its name (e.g., Cat/Hen/Bee — 3 letters).
- An animal with a longer name: Hippopotamus (12 letters).

Given: Two names — Mahesh and Kartik.

Step 1 — Count letters in each name:

- M-A-H-E-S-H → Mahesh has $6$ letters.
- K-A-R-T-I-K → Kartik has $6$ letters.

Step 2 — Compare:
$$6 = 6$$

Both names have the same number of letters.

Final Answer: Neither name is longer — Mahesh and Kartik both have 6 letters each. Their names are of equal length.

Note: This is an activity-based question. The answers will vary for each student depending on the names of their friends. Below is a model solution using sample names.

Sample names (for illustration): Anita, Arjun, Bhavna, Chetan, Deepa, Divya, Farhan, Geeta

Letter count for each name:

| Name | Number of Letters |
|---|---|
| Anita | 5 |
| Arjun | 5 |
| Bhavna | 6 |
| Chetan | 6 |
| Deepa | 5 |
| Divya | 5 |
| Farhan | 6 |
| Geeta | 5 |

(a) Longest and Shortest names:
- Longest names (6 letters): ✓ Bhavna, Chetan, Farhan
- Shortest names (5 letters): ✗ Anita, Arjun, Deepa, Divya, Geeta
*(Students tick and cross based on their own list.)*

(b) Starting letter of your name:
For example, if your name is Deepa, the starting letter is D.

(c) Names with the same starting letter as yours:
If starting letter is D → Deepa, Divya → 2 names.

(d) Most used starting letter:
From the sample: A (Anita, Arjun) = 2; D (Deepa, Divya) = 2; others = 1 each.
Most used: A or D — 2 names each.
*(Students find this from their own list.)*

(e) Names with the same ending letter:
- Ending in 'a': Anita, Bhavna, Deepa, Divya, Geeta → 5 names end in 'a'.

(f) Letters not used as starting letters:
From A to G, the letters used are: A, B, C, D, F, G.
Not used: E (and all letters from H to Z that are not starting letters of any name in the list).

Final Note: Students should fill in this activity using the actual names of their classmates/friends.

Given: Roll number 43 → FORTY THREE → 10 letters.
Roll number 17 → SEVENTEEN.

Step 1 — Count letters in SEVENTEEN:
S-E-V-E-N-T-E-E-N
$$= 9 \text{ letters}$$

Answer for Jojo: SEVENTEEN has 9 letters.

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(a) My roll number:
*(This is a personal activity. Below is a model.)*

Suppose roll number = 25
Number name = TWENTY FIVE
- TWENTY: T-W-E-N-T-Y = 6 letters
- FIVE: F-I-V-E = 4 letters
- Total = $6 + 4 =$ 10 letters

Students write their own roll number and count the letters in its number name.

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(b) Some numbers and their number names with letter counts:

| Number | Number Name | Letter Count |
|---|---|---|
| 12 | Twelve | 6 |
| 15 | Fifteen | 7 |
| 20 | Twenty | 6 |
| 31 | Thirty One | 9 |
| 45 | Forty Five | 9 |
| 56 | Fifty Six | 8 |
| 72 | Seventy Two | 10 |
| 99 | Ninety Nine | 9 |

Final Answer: SEVENTEEN has 9 letters. Students complete parts (a) and (b) using their own roll numbers and chosen numbers.

Given: 56 → FIFTY SIX → F-I-F-T-Y (5) + S-I-X (3) = 8 letters.

Task: Find all numbers between 1 and 99 whose number names also have exactly 8 letters.

Method: Count letters in each number name carefully.

Numbers with 8 letters:

| Number | Number Name | Count |
|---|---|---|
| 42 | Forty Two | F-O-R-T-Y (5) + T-W-O (3) = 8 |
| 51 | Fifty One | F-I-F-T-Y (5) + O-N-E (3) = 8 |
| 52 | Fifty Two | F-I-F-T-Y (5) + T-W-O (3) = 8 |
| 53 | Fifty Three | F-I-F-T-Y (5) + T-H-R-E-E (5) = 10 ✗ |
| 56 | Fifty Six | F-I-F-T-Y (5) + S-I-X (3) = 8 ✓ |
| 61 | Sixty One | S-I-X-T-Y (5) + O-N-E (3) = 8 |
| 62 | Sixty Two | S-I-X-T-Y (5) + T-W-O (3) = 8 |
| 66 | Sixty Six | S-I-X-T-Y (5) + S-I-X (3) = 8 |
| 41 | Forty One | F-O-R-T-Y (5) + O-N-E (3) = 8 |
| 46 | Forty Six | F-O-R-T-Y (5) + S-I-X (3) = 8 |

Final Answer: Numbers between 1 and 99 with 8 letters in their number names include:
$$41, 42, 46, 51, 52, 56, 61, 62, 66 \text{ (and similar combinations)}$$

*Observation: Numbers in the forties (forty + 3-letter word), fifties (fifty + 3-letter word), and sixties (sixty + 3-letter word) tend to give 8-letter names.*

Concept: We need to find which number between 1 and 99 has the most letters in its number name.

Check long candidates:

| Number | Number Name | Letter Count |
|---|---|---|
| 13 | Thirteen | 8 |
| 15 | Fifteen | 7 |
| 17 | Seventeen | 9 |
| 19 | Nineteen | 8 |
| 73 | Seventy Three | S-E-V-E-N-T-Y (7) + T-H-R-E-E (5) = 12 |
| 79 | Seventy Nine | S-E-V-E-N-T-Y (7) + N-I-N-E (4) = 11 |
| 83 | Eighty Three | E-I-G-H-T-Y (6) + T-H-R-E-E (5) = 11 |
| 93 | Ninety Three | N-I-N-E-T-Y (6) + T-H-R-E-E (5) = 11 |
| 73 | Seventy Three | 7 + 5 = 12 |

Checking 73 carefully:
SEVENTY = S-E-V-E-N-T-Y = 7 letters
THREE = T-H-R-E-E = 5 letters
Total = $7 + 5 =$ 12 letters

Final Answer: The number with the longest name between 1 and 99 is 73 (Seventy Three) with 12 letters.