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Hi, not sure how to tackle the working out for this question:
I take a tablet every 10 days. If I take my first tablet on Monday and have 25 tablets,
on what day will I take the last tablet.
The answer my teacher gave is a Wednesday. Should I use modular arithmetic to solve, very stuck. Thank you.
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O-o-p-s !
I agree with the @greenestamps notice, saying that the period in this problem is 10 days, not 9.
@greenestamps, thanks for noticing my fault.
Having it, I re-wrote my solution, so now you see the updated version.
+-------------------------------------------------------------------------------+
| To start solving, notice that taking a tablet every 10 days means |
| that the process of taking tablets is periodical with the period of 10 days. |
+-------------------------------------------------------------------------------+
Imagine that the days are coded in this natural way, using numbers from 1 to 7
instead of the days standard naming
Mo Tu We Th Fr Sa Su (*)
1 2 3 4 5 6 7
Next, imasgine that you have long sequence of these numbers, repeating in this natural order
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 . . . .
Then your day in this sequence is this coding number (10*24+1 mod 7)
(i.e. 24 intervals of 10 days plus the next day, and the sum is taken modulo 7).
Multiply 10*24 and add 1. You will get 241.
Find the remainder after division 241 by 7.
The division is 241 = 34*7 + 3.
Thus the remainder is 3.
In other words, (10*24+1 mod 7) = 3.
The remainder "3" is the code for the 3-rd day in the sequence (*).
Hence, you will take your last tablet on Wednesday.
Solved.
Nice problem.
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Yes, the idea is correct to use modular arithmetic.
But still there is an underwater stone (a trap) which should be treated accurately.
The stone is to determine CORRECTLY that the day of interest is 24*10+1 (not 25*10).
After that, applying modular arithmetic will lead you to the answer quickly and straightforward.