Math Monday - Adventures in Puzzlevania 2
Today’s Puzzle
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?
Friday’s Puzzle - Tipping the Scales
You have ten bags of coins, each containing 1000 coins. One of the bags, though, is full of counterfeit coins - instead of weighing 1 gram each, they weigh 1.1 grams each. You have a digital scale, but you can only use it once.* How do you identify which bag contains the counterfeit coins?
[SPOILER] Answer to Friday’s Puzzle
Label the bags 1 through 10. Take 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3, and so on through bag 10.
You now have a total of 1+2+3+4+5+6+7+8+9+10=55 coins. Place them all on the scale. If all the coins were real, we would expect the total weight to be 55 grams. But since some of the coins are counterfeit, the final weight is slightly higher. The decimal of the weight will tell you which bag contains the counterfeit coins.
If bag 3 contained the counterfeits, for example, then the final weight would be 55.3 grams, since each of the 3 coins from bag 3 would contribute an extra 0.1 grams. (If the final weight is 56 grams, we know that bag ten contains the counterfeits, because 10 x 0.1 = 1.)