EGGS!!

Algebra Level 1

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. The farmer says she doesn't know, but she remembers somethings from various ways she tried packing the eggs.

When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over.

How many eggs did she have?

301 420 540 240

2 solutions

丁大喵 By丁丁猫
Nov 9, 2018

for i in range(10000): if i % 2 == 1 and i % 3== 1 and i % 4 == 1 and i % 5 == 1 and i % 6 == 1: if i % 7 == 0: print(i)

X X
Jul 22, 2018

Relevant wiki: Chinese Remainder Theorem

Let there are $x$ eggs.

"When she put the eggs in groups of two, three, four, five, and six there was one egg left over",this means when $x$ is devided by $\gcd(2,3,4,5,6)=60$ leaves a remainder of 1.

"When she put them in groups of seven they ended up in complete groups with no eggs left over",this means $x$ is a multiple of 7.

Solve for $x$ and get $x\equiv301\pmod{420}$

EGGS!!

2 solutions

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