- #1
coreyB
- 9
- 0
Homework Statement
i'm sure everyone has seen this:
Solve the following ancient Indian problem: If eggs are removed from a basket 2, 3, 4,
5, and 6 at a time, there remain, respectively, 1, 2, 3, 4, and 5 eggs. But if the eggs are
removed 7 at a time, no eggs remain. What is the least number of eggs that could have
been in the basket?
Homework Equations
x=1%2
x=2%3
x=3%4 implies %2 (dropped)
x=4%5
x=5%6 impies %2,3 (dropped)
x=0%7
this leaves just four equations.
The Attempt at a Solution
x=1%2
x=2k+1
x=2%3
2k+1=2%3
2k=1%3
k=2%3
k=3p+2
and x=2k+1 so x= 2(3p+2)+1 = 6p+5
x=4%5
6p+5=4%5
6p=4%5
p=4%5
p=5j+4
and x=6p+5 so x=6(5j+4)=5 = 30j+29
30j+29
x=0%7
30j+29=0%7
30j=6%7
j=3%7
j=7r+3
and x=30j+29 so x=30(7r+3)+29=210r+119
so x=119%210 = 119.
how does this look? feedback appreciated.