SANTACLAUSSANTACLAUSSAN... If this pattern of letters was to continue to the 2024th letter, how many times in all does the letter A appear?

Question

SANTACLAUSSANTACLAUSSAN... If this pattern of letters was to continue to the 2024th letter, how many times in all does the letter A appear?

Answer 1

Hi Yfut, I'm Emma. Here are the steps you'd take to solve this problem. Please let me know if you have any questions about this explanation!

1. Identify the pattern of letters. It looks like you have the words "Santa Claus," a phrase consisting of ten letters and three letter "As."
2. SANTA CLAUS
3. The phrase will repeat to the 2024th letter, so it will repeat (2024 ÷ 10) times. This equation will come out to a decimal, meaning that the 2024th letter is partway through the pattern.
4. You need to find the closest number to 2024 that's evenly divisible by 10. If you calculate (2020 ÷ 10), you get a whole number, meaning that the entire phrase repeats that many times. In addition, you're left with four letters left over. You now know that your 2024th letter will be "T," the fourth letter of your phrase "SANTA CLAUS."
5. The last step is to figure out how many letter "As" you have in your 2024 letters. Take your number of total repetitions of "SANTA CLAUS" and multiply it by the number of times "A" appears within that phrase. This gives you all of the "As" in your first 2020 letters. Add to this the one letter "A" that occurs in your four left over letters "SANT."

Calculate: (3 x (2020 ÷ 10)) + 1 to get your answer.