## saifkhansk 3 years ago How can you find the 1000 letter in " Thursday " ?

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1. yummydum

umm...what?

2. saifkhansk

How do you find the 1000th letter in the word thursday if you keep counting

3. zzr0ck3r

1000/8 what is the remainder?

4. saifkhansk

125

5. Doman

it shoulld be less than 8

6. saifkhansk

no 1000/8 equals 125

7. lgbasallote

the remainder should be less than 8*

8. Doman

remainder is zero

9. zzr0ck3r

if the remainder was 0 would it not be y?

10. Doman

it would be y

11. zzr0ck3r

Sorry, I was not trying to give the answer, I just thought you guys were saying its wrong so I wanted to make sure...

12. saifkhansk

how is it Y

13. saifkhansk

?

14. zzr0ck3r

imagine we were counting to 16 16/8 has a remainder of 0 notive the 16 letter is y

15. zzr0ck3r

notice*

16. saifkhansk

Where is the 16 coming from

17. zzr0ck3r

just an example.

18. saifkhansk

Can you list me the steps pleasee i really need help?

19. zzr0ck3r

i think @KingGeorge is prob doing that.

20. KingGeorge

For example, look at the sequence of letters thursdaythursdaythursdaythursdaythursdaythursday 8 16 24 32 40 48 Notice that every time the letter "y" appears, you see that it is in a position divisible by 8. This is because there are 8 letters in the word "thursday."

21. KingGeorge

It's basically saying the same thing as labeling each number in the set $\{1,2,3,4,5,6,7,8,9,...,997,998,999,1000\}$With a letter. You start with the pattern "thursday" and every 8 letters, you repeat that pattern.

22. saifkhansk

yeah but isnt it 1000/8 which then equals 125 what do you do after that

23. KingGeorge

This means that since your word is 8 letters long, every eighth letter will be "y" starting with the number 8. What you want to do, is find the remainder, and not the quotient. So you have ${1000}=8\cdot125+0$So your quotient is 125, and your remainder is 0. Somewhat unintuitively, this means that the 8th letter in "thursday" will be the 1000th letter overall.

24. saifkhansk

what if i wanna know the 1000th letter of Tuesday

25. zzr0ck3r

1000/7 remainder is what?

26. saifkhansk

142

27. zzr0ck3r

if its three its the third letter, 4 then 4th, 0 then last

28. saifkhansk

142.8571429

29. KingGeorge

"tuesday" only has 7 letters. So in this case, you want to find $1000=7\cdot q+r$you have $$q=142$$. What is $$r$$?

30. zzr0ck3r

we want remainder not dec

31. KingGeorge

$1000=7\cdot142+r$$1000=994+r$Can you tell me what $$r$$ is?

32. saifkhansk

idk

33. KingGeorge

$1000-994=994-994+r$Does this help?

34. zzr0ck3r

1000- 142*7 = r

35. zzr0ck3r

and we will have the rth letter

36. saifkhansk

Okay thanks