The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 42 letters. Give a 7-digit number name which has the maximum number of letters.

Question

Homi · Accepted Answer

We need to find a 7-digit number whose name has the most letters.

Step 1 — Understand the Indian Number System

A 7-digit number has seven places. We read it using lakhs, thousands, and hundreds. For example, 10,30,285 is "Ten lakhs thirty thousand two hundred eighty five". We will find the number that gives the longest name.

Step 2 — Count letters for number words

Let us list the number of letters for common number words. This helps us choose words with more letters.

Words for digits (1-9):

One: 3 letters
Two: 3 letters
Three: 5 letters
Four: 4 letters
Five: 4 letters
Six: 3 letters
Seven: 5 letters
Eight: 5 letters
Nine: 4 letters

Words for numbers (10-19):

Ten: 3 letters
Eleven: 6 letters
Twelve: 6 letters
Thirteen: 8 letters
Fourteen: 8 letters
Fifteen: 7 letters
Sixteen: 7 letters
Seventeen: 9 letters
Eighteen: 8 letters
Nineteen: 8 letters

Words for tens (20-90):

Twenty: 6 letters
Thirty: 6 letters
Forty: 5 letters
Fifty: 5 letters
Sixty: 5 letters
Seventy: 7 letters
Eighty: 6 letters
Ninety: 6 letters

Words for place values:

Hundred: 7 letters
Thousand: 8 letters
Lakh: 4 letters

Step 3 — Maximize letters for each part of the number name

A 7-digit number is written as $L_1 L_2, T_1 T_2, H_1 U_1 U_2$ . Its name is " $L_1 L_2$ lakhs $T_1 T_2$ thousand $H_1$ hundred $U_1 U_2$ ". We will choose digits for each part to get the most letters.

First, let us find the maximum letters for a two-digit number (XX). "Seventy-seven" has $7+5 = \mathbf{12}$ letters. "Seventy-eight" also has $7+5 = \mathbf{12}$ letters. "Seventeen" has $\mathbf{9}$ letters. These are the longest two-digit number names.

Next, let us find the maximum letters for a single-digit number (X). "Three" has $\mathbf{5}$ letters. "Seven" has $\mathbf{5}$ letters. "Eight" has $\mathbf{5}$ letters. These are the longest single-digit number names.

Now, we apply this to each part of the 7-digit number:

Lakhs part ( $L_1 L_2$ lakhs): We choose "seventy-seven" for the number. Letters for "seventy-seven": 12 letters. Letters for "lakhs": 4 letters. Total letters for lakhs part: $12 + 4$

$\boxed{16 \text{ letters}}$
Thousands part ( $T_1 T_2$ thousand): We choose "seventy-seven" for the number. Letters for "seventy-seven": 12 letters. Letters for "thousand": 8 letters. Total letters for thousands part: $12 + 8$

$\boxed{20 \text{ letters}}$
Hundreds part ( $H_1$ hundred): We choose "seven" for the number. Letters for "seven": 5 letters. Letters for "hundred": 7 letters. Total letters for hundreds part: $5 + 7$

$\boxed{12 \text{ letters}}$
Units part ( $U_1 U_2$ ): We choose "seventy-seven" for the number. Total letters for units part:

$\boxed{12 \text{ letters}}$

Step 4 — Construct the number and count total letters

We combine the parts we chose. The number is 77,77,777. Its name is "Seventy-seven lakhs seventy-seven thousand seven hundred seventy-seven".

Let us add the letters from all parts. Total letters = Letters from lakhs part + Letters from thousands part + Letters from hundreds part + Letters from units part.

$16 + 20 + 12 + 12$ $= 36 + 12 + 12$ $= 48 + 12$

$\boxed{60 \text{ letters}}$

The number name with the maximum number of letters is "Seventy-seven lakhs seventy-seven thousand seven hundred seventy-seven". It has 60 letters.

Answer

(i) The 7-digit number is 77,77,777. (ii) The number name is Seventy-seven lakhs seventy-seven thousand seven hundred seventy-seven. (iii) The maximum number of letters in its name is 60.

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