Thread: Math egg puzzle Help

a peddler is taking edge to the market to sell. The eggs are in a cart that can hold 500 eggs. If the eggs are removed fom the cart 2 3 4 5 or 6 at a time 1 egg s alwas left over If the eggs are removed 7 at a time no eggs are left over how many eggs are their in the cart?

Hello, Dragon!

A peddler is taking eggs to the market to sell.
The eggs are in a cart that can hold 500 eggs.
If the eggs are removed fom the cart 2, 3, 4, 5 or 6 at a time,
. . one egg is always left over.
If the eggs are removed 7 at a time, no eggs are left over.
How many eggs are their in the cart?

Let be the number of eggs.

The LCM of 2, 3, 4, 5 and 6 is .
. . Hence, (and any multiple of 60) is divisible by 2, 3, 4, 5 and 6.
To have a remainder of 1, must be of the form: .
. . for some positive integer .
That is: [1]

Since is divisible by


If you're familiar with Modulo Arithmetic: .

Reduce: .

Multiply by 2: .

Hence, is of the form: for some integer .
That is: [2]


Substitute [2] into [1]: .

Since , then

Therefore: .


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If you're not familiar with Modulo Arithmetic,
. . it can be solved with "ordinary" algebra.
It just takes longer.