### Brain Teasers

# Cookie Crunchers

Cassie, Jon, Luke, Maria, and Sahas baked a batch of 36 cookies, two-thirds of which were chocolate chip. The rest were plain. They each ate at least one right away. The cookies were so delicious, only one-and-a-half dozen are left, of which half are plain.

1. Cassie is allergic to chocolate.

2. Luke ate twice as many chocolate chip cookies as plain cookies.

3. Sahas and Maria each ate as many cookies as Luke and Cassie combined.

4. Sahas ate more chocolate chip cookies than Maria.

If all the cookies were eaten by the bakers themselves, how many cookies of each kind did each person eat?

1. Cassie is allergic to chocolate.

2. Luke ate twice as many chocolate chip cookies as plain cookies.

3. Sahas and Maria each ate as many cookies as Luke and Cassie combined.

4. Sahas ate more chocolate chip cookies than Maria.

If all the cookies were eaten by the bakers themselves, how many cookies of each kind did each person eat?

### Hint

1. Determine the distribution of the types of cookies that were eaten. Then solve from there.2. Make a chart to eliminate the impossibilities.

### Answer

Cassie: 1 plainJon: 6 chocolate chip

Luke: 2 chocolate chip and 1 plain

Maria: 3 chocolate chip and 1 plain

Sahas: 4 chocolate chip

Of the 36 cookies baked, two thirds, or 24, were chocolate chip and 12 were plain.

Of the 1 1/2 dozen, or 18, cookies remaining, 9 are chocolate chip and 9 are plain.

So, of the cookies eaten, 24 - 9 = 15, which were chocolate chip, and 12 - 9 = 3, which were plain.

Both Cassie and Luke must each have eaten at least 1 plain cookie. Sahas and Maria each ate the same number of cookies, but Sahas ate more chocolate chip cookies than Maria, so one of Maria's cookies must have been plain. That left Cassie with 1 plain cookie, and Luke with 1 plain and 2 chocolate chip cookies. Between them, Luke and Cassie ate 4 cookies, so Sahas ate 4 chocolate chip cookies and Maria ate 3 chocolate chip cookies and 1 plain cookie. Jon must have eaten the other 6 chocolate chip cookies.

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