Once upon a time, there was a boy named Tom who loved to solve puzzles. He had a book of secret codes that he used to write messages to his friends. He also liked to decipher the codes that his friends sent him.
One day, he received a letter from his cousin Lily, who lived in another city. She had written a message in a secret code that Tom had never seen before. It looked like this:
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99
Tom was curious and excited. He wanted to know what Lily had written to him. He took out his book of secret codes and looked for clues. He found a page that said:
“To decode this message, you need to know two things: the key and the rule. The key is a number that tells you how to change each number in the code. The rule is a mathematical operation that tells you what to do with the key and the number. For example, if the key is 2 and the rule is subtraction, then you need to subtract 2 from each number in the code. If the key is 3 and the rule is multiplication, then you need to multiply each number by 3 in the code. To find the key and the rule, you need to look for patterns in the code.”
Tom studied the code carefully. He noticed that the numbers were all odd and increased by 2. He wondered if that was a pattern. He tried to subtract 2 from each number, but that didn’t make sense. He tried to divide each number by 2, but that didn’t work either. He tried to add 2 to each number, but that was too easy. He tried to multiply each number by 2, but that was too hard.
He scratched his head and thought hard. He decided to try something else. He looked at the first and the last number in the code. He noticed that they were both divisible by 3. He wondered if that was a clue. He tried to divide each number by 3, but that didn’t make sense. He tried to multiply each number by 3, but that didn’t work either. He tried to add 3 to each number, but that was too easy. He tried to subtract 3 from each number, but that was too hard.
He sighed and felt frustrated. He decided to try one more thing. He looked at the second and the second last number in the code. He noticed that they were both divisible by 5. He wondered if that was the key. He tried to divide each number by 5, but that didn’t make sense. He tried to multiply each number by 5, but that didn’t work either. He tried to add 5 to each number, but that was too easy. He tried to subtract 5 from each number, and he got a surprise.
He saw that the numbers became even and decreased by 10. He realized that he had found the key and the rule. The key was 5 and the rule was subtraction. He quickly wrote down the new numbers:
-2 -8 -18 -28 -38 -48 -58 -68 -78 -88 -98 -108 -118 -128 -138 -148 -158 -168 -178 -188 -198 -208 -218 -228 -238 -248 -258 -268 -278 -288 -298 -308 -318 -328 -338 -348 -358 -368 -378 -388 -398 -408 -418 -428 -438 -448 -458 -468 -478 -488 -498
He smiled and felt proud. He had cracked the code. He looked at his book of secret codes and found another page that said:
“To read the message, you need to know the alphabet code. The alphabet code is a way of assigning a letter to each number. For example, A is 1, B is 2, C is 3, and so on. To find the letter that corresponds to each number, you need to add 26 to the number until it is between 1 and 26. For example, if the number is -2, you need to add 26 to get 24, which is X. If the number is -8, you need to add 26 twice to get 44, which is R. If the number is -18, you need to add 26 three times to get 60, which is Z. And so on.”
Tom followed the instructions and wrote down the letters that matched the numbers:
X R Z J T D P B L V F Z J T D P B L V F Z J T D P B L V F
He looked at the letters and saw that they repeated every 10 letters. He wondered if that was another pattern. He tried to rearrange the letters in groups of 10, but that didn’t make sense. He tried to rearrange the letters in groups of 5, but that didn’t work either. He tried to rearrange the letters in groups of 2, but that was too easy. He tried to rearrange the letters in groups of 3, and he got another surprise.
He saw that the letters formed words that he could read. He realized that he had solved the puzzle. He quickly wrote down the words:
X R Z J T D P B L V F Z J T D P B L V F Z J T D P B L V F
XRZ JTD PBL VFZ JTD PBL VFZ JTD PBL VFZ
HUG KID YOU BIG KID YOU BIG KID YOU
He read the message and felt happy. He understood what Lily had written to him. She had sent him a hug and called him a big kid. He knew that she meant it as a compliment. She was proud of him for being smart and brave. She was his favorite cousin and his best friend.
He decided to write back to her. He took out his magic pen and wrote a message in a secret code that he had invented. He hoped that she would be able to decode it. He wrote:
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100
He put the letter in an envelope and mailed it to Lily. He waited for her reply. He wondered if she would like his puzzle. He wondered if she would send him another one. He wondered what adventures they would have together.
He smiled and felt excited. He loved to solve puzzles. He loved to write messages to his friends. He loved to have fun.
The End
