The Torah Math Project
The Four Camps
In the desert the tribes were divided into four camps. The four camps were placed around the Mishkan. The Torah gives us the number of people in each tribe and the total number of people in each of the four camps.
Question: This chart gives you the totals for each camp but only some of the tribes. Using the numbers given, figure out which of the tribes goes into each camp.
North Camp
Dan 62,700
__________ ___________
__________ ___________
Total for North Camp: 157,600
East Camp
Yehudah 74,600
__________ ___________
__________ ___________
Total for East Camp: 186,400
South Camp
Reuven 46,500
__________ ___________
__________ ___________
Total for South Camp: 151,450
West Camp
Ephraim 40,500
__________ ___________
__________ ___________
Total for West Camp: 108,100
Answer: How to solve this.
- You know the camp for 4 of the tribes, so cross them of the list. That leaves 8 tribes to place.
Reuven 46,500
Shimeon 59,300
Gad 45,650
Issachar 54,400
Zevulun 57,400
Ephraim 40,500
Menashe 32,200
Benjamin 35,400
Dan 62,700
Asher 41,500
Naphtali 53,400
Yehudah 74,600
- Pick one camp. We will use the North Camp for example.
Take the total number from the Camp and substract the number from the one tribe that you are given.
Total for North Camp 157,600 – Tribe of Dan 62,700 = 94,900
This tells you that the other two tribes have to add up to 94,900. Now try to figure out which two tribes add up to 94,900. It may be easier to look only at the last three numbers to see which two will add up to 900 (or 1900).
Reuben 46,500
Simeon 59,300
Gad 45,650
Issachar 54,400
Zebulun 57,400
Ephraim 40,500
Manasseh 32,200
Benjamin 35,400
Dan 62,700
Asher 41,500
Naphtrali 53,400
Yehudah 74,600
There are several combinations that will end in 900, but all of them include Asher, so you know that one of the other two is Asher with 41,500. Now subtract that amount from 94,900.
94,900 – 41,500 = 53,400
So the remaining tribe has to have 53,400 which makes it Naphtali. Now you can remove Asher and Naphtali from the list which makes figuring out the others easier.
Reuben 46,500
Simeon 59,300
Gad 45,650
Issachar 54,400
Zebulun 57,400
Ephraim 40,500
Manasseh 32,200
Benjamin 35,400
Dan 62,700
Asher 41,500
Naphtrali 53,400
Yehudah 74,600
