WORD WEDNESDAY - The good, the bad, and the weird friend who keeps throwing parties
Today’s Puzzle
Your very quirky friend (yes, the same one who made you solve logic puzzles at her birthday) has invited you over for a dinner party. You are skeptical (understandably so), but you decide to give her another chance. Unfortunately, when you arrive, you discover your fears were justified. Posted on the door is the following:
CONDITIONS OF ENTRY - In the pairs of words below, the left words are examples of BAD words and the right words are examples of GOOD words. Any guests heard using BAD words at tonight’s dinner will be thrown out immediately.
- in / out
- jump / hop
- reign / rule
- solution / answer
- ajar / open
- liberty / freedom
Can you identify what all the bad words have in common and survive the dinner? (It could be something about their meaning, spelling, pronunciation, or something else entirely.)
Monday’s Puzzle - Adventures in Puzzlevania 2
You find yourself, once again, in the magical land of Puzzlevania. This time, you are here to purchase some baked goods from the famous Modulus Muffin Man.
You walk into the Muffin Man’s shop and ask for exactly 13 muffins - a baker’s dozen.
“I’m sorry,” he says. “I only sell muffins in packs of 6, 9, and 20.”
You ponder this for a moment. “So I could get, for example, 15 muffins with a 6-pack and a 9-pack?”
“Exactly,” he responds.
This gets you thinking - what is the largest number of muffins you cannot buy using combinations of 6, 9, and 20?
[SPOILER] Answer to Monday’s Puzzle
43.
Let’s start by just considering different combinations of 6 and 9, with no 20’s. We can get all possible multiples of 3, starting with 6, with just those two numbers: 6+6=12, 6+9=15, 6+6+6=18, 6+6+9=21, etc.
Now, let’s consider the 20-pack. You could get just a 20-pack, or you could get a 20-pack plus different combinations of 6 and 9. This means you could get 26, 29, 32, 35, 38, etc. Notice that all of these numbers are two more than a multiple of 3 (20=18+2, 26=24+2, 29=27+2, and so on). Mathematically speaking, we say 20 modulo 3 is 2. We could keep going forever, generating all possible numbers that are two more than a multiple of 3, starting with 26.
Now let’s see what happens when we add another 20-pack. Two 20’s would start us out at 40, and then we could add various combinations of 6 and 9 to get 46, 49, 52, 55, 58. What do you notice about these numbers? They’re all one more that a multiple of 3. This means that starting with 46, we can generate all numbers that are one more than a multiple of 3.
So where does that leave us? We can get all of the multiples of 3 bigger than (and including) 6, all the multiples of 3 plus 1 bigger than (and including) 46, and all multiples of 3 plus 2 bigger than (and including) 26. Well, all numbers are either multiples of 3, multiples of 3 plus 1, or multiples of 3 plus 2. So, we just need to look for the largest number we can’t make using one of these methods, which is 43.