Puzzle of the Week and Das Solutions to Last Week

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

Conor Naughton | The Rock at Boston College

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