30 Brothers each attend the daily sunset service 4 times a week. Whilst they are all present on Sunday, the numbers present throughout the week varies from day to day. Alan wanted to learn more about the religion. He knew the Brothers were in great demand for their knowledge and wisdom but he could only make the Friday service. Checking the notice board outside the steps, he saw the following:
-The Brothers attending on Monday, also go on Tuesdays and Wednesdays.
-Twice as many go on Wednesday as Monday.
-The number present on Tuesday is the sum of the number on Wednesday and Thursday.
-Those attending on Friday or Saturday do not go to the Thursday service.
-Half as many go on Thursday as on Monday.
-They don't all go on Tuesday.
How many Brothers would be at the temple for him to talk to?
This surely is not psychology.
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To solve this problem, let's go through the given information step by step and use logic to deduce the number of brothers present on Friday.
1. The brothers attending on Monday also go on Tuesdays and Wednesdays.
Let's assume the number of Brothers attending on Monday is "M." So, the number of Brothers attending on Tuesday and Wednesday will also be "M."
2. Twice as many brothers go on Wednesday as on Monday.
From the previous point, we know that the number of Brothers attending on Wednesday is "M." So, based on this information, the number of Brothers attending on Monday will be half of that, which is "M/2."
3. The number present on Tuesday is the sum of the numbers on Wednesday and Thursday.
Let's assume the number of Brothers attending on Tuesday is "T." According to this information, T = M + M, which simplifies to T = 2M.
4. Those attending on Friday or Saturday do not go to the Thursday service.
This information tells us that the number of Brothers attending on Thursday will be different from those attending on Friday or Saturday. So, we have a new variable, let's call it "Th," for the number of Brothers attending on Thursday.
5. Half as many brothers go on Thursday as on Monday.
Based on this information, Th = M/2.
6. They don't all go on Tuesday.
This information implies that the number of Brothers attending on Tuesday is less than the total number of Brothers.
Now, let's combine the information we have gathered:
From point 3, we know that T = 2M.
From point 5, we know that Th = M/2.
Since Th is half of T, and T is 2M, we can infer that Th = M/2 = T/4.
If we let the number of Brothers attending on Friday be "F," then the number of Brothers attending on Saturday will also be "F" because there's no overlap with Thursday.
So now, let's summarize the number of Brothers attending each day:
Monday: M
Tuesday: 2M
Wednesday: M
Thursday: Th = M/2
Friday: F
Saturday: F
Sunday: Unknown, but we'll come back to this.
Now, let's consider the Sunday service. We're told that all the Brothers are present on Sunday, so the total count of Brothers attending each service from Monday to Saturday must add up to the total number of Brothers.
M + 2M + M + M/2 + F + F = Total number of Brothers
Simplifying this equation, we get:
5M/2 + 2F = Total number of Brothers
However, we still need more information to calculate the exact number of Brothers. Unfortunately, the given information doesn't provide any direct relationship or values for M and F.
Therefore, without additional information, we cannot determine the exact number of Brothers attending the temple on Friday.