**Solutions to Last Week’s Riddle**

(1) Knowing there are 3 children and the **product is 72** we can list every combination of products that give us 72 (I’ll leave that to you). Since the sum of the ages of the children is not enough information, we know that there must be **at least 1 repeated sum**. I’ll just tell you that there is only 1 repeated sum: 14

**(a) ****3 + 3 + 8 = 14 and 3 x 3 x 8= 72**

**(b) ****2 + 6+ 6 = 14 and 2 x 6 x 6 = 72**

When Pauli says “My **youngest**…”, Heisenberg knows option (b) is the correct choice

**Answer: The children are ages 2, 6, and 6**

(2) We are given the number of small bottles: 7, the number of large bottles: 18, and the total number of medicine tablets: 233. Therefore we have the following equation:

**7X + 18Y = 233**

**X = number of tablets in small bottles**

**Y = number of tablets in large bottles**

We are also given that Y > X. Now the trick here is to find the max and min value of Y:

Let X = Y (this represents the low end of Y). Plug this into our equation to get:

**7Y + 18Y = 25Y = 233 ****=> Y = 9.32 **

Since we are dealing with **integer** **numbers** (the medicine tablets don’t come cut in half or ¼’s) and the fact that Y > X we know that y must be **greater than or equal** to 10. Now for the maximum value of Y: Plug X = 1 into our equation to get:

**7 + 18Y = 233 ****=> Y = 12.55**

Again we are dealing with **integer numbers** so the max value of Y is 12 (Y cannot be 13 because 18 x 13 = 234, which is more than our original tablet count).

Now we have 3 values for Y: 10, 11, 12. Plugging each one into our equation and we get the following X values: 7.57, 5, 2.43 respectively. Again we’re using **integer numbers ** only so the correct Y value must be 11

**Answer: There are 5 medicine tablets in the small bottles and 11 tablets in the large bottles. Disaster averted! **

**New Puzzle**

This Puzzle is Easier to Solve while drinking:

Connect all 9 dots using **ONLY 4 lines** and **NEVER** picking up your pencil/pen/crayon/paint brush/any other writing device/beer