On each day of the seven days of Chag Sukkos the Cohanim offered special sacrifices in the Bais HaMikdash of 14 sheep (כבשים), two rams(אילים), one goat (שעיר). Also, they offered cows (פרים), but this number changed each day. The count started with 13, decreased by one each day until the final day, when 7 cows were offered.
Determine the Following:
- The total number of cows offered during Sukkos ____________ (F+L)/2 * I (see math formula below)
- Total number of goats ____________
- Total number of rams ____________
- Total number of sheep ____________
- The total number of Sukkos offerings ____________
The 24 groups (משמרות) of Cohanim served equally in the Bais HaMikdash regarding the holiday offerings during the 3 major holidays. Thus, on Sukkos they each took turns offering the total number Sukkos offerings. Each day the groups would first offer (sequentially) the rams, the goats, and the sheep. However, of the 14 sheep offered each day, some groups would offer one sheep and some offered two sheep.
Determine each day how many משמרות offered two sacrifices:
Hint: figure out how many offerings each of the seven days
Math Formula
One can quickly add a consecutive series of numbers using a simple formula:
- Determine the average value of the numbers by adding the first and last number in the sequence together and then divide by 2. F(irst) + L(ast) / (divided by) 2 (F+L)/2
- Determine the actual number of consecutive numbers (integers) I(integers)
- Multiply the answer from step one times the answer from step 2 (F+L)/2*I
Simple example: sum of 4, 5, 6, 7, 8
- F+L/2 Add 4 plus 8 (12) and divide by 2 = 6
- Total number of Integers = 5
- (F+L)/2 * I 6 X 5 = 30
Example: sum of all integers from 1 to 100
- (F+L)/2 Add 1 plus 100 (101) and divide by 2 = 50.5
- Total number of Integers = 100
- (F+L)/2 * I 50.5 X 100 = 5,050
