Minute Mystery: The Cookie Jar

Day 3:

Let z​ be the number of cookies at the start of Day 3. On Day 3, Carl eats half of z​ plus one extra cookie, and the jar ends up empty. This gives the equation:

z = z/2 + 1

z - z/2 = 1

2z/2 - z/2 = 1

z/2 = 1

z = 2

At the beginning of Day 3, there were 2 cookies.

Day 2:

Let y​ be the number of cookies at the start of Day 2. At the end of Day 2, after following the rule, the jar is left with 2 cookies. The consumption on Day 2 is:

y/2 + 1

Thus, the remaining cookies after Day 2 are:

y - (y/2 +1) = 2

Simplify:

2y/2 - (y/2 + 2/2) = 2

y/2 - 1 = 2

y/2 = 3

y = 6

At the beginning of Day 2, there were 6 cookies.

Day 1:

Let x​ be the initial number of cookies in the jar. At the end of Day 1, after consuming half plus one, the jar is left with 6 cookies. This gives:

x - (x/2 +1) = 6

Simplify:

2x/2 - (x/2 + 2/2) = 6

x/2 - 2/2 = 6

x - 2 = 12

x = 14

There were originally 14 cookies in the jar.