Subtle Coolness

So, the riddle does have a solution. I have just been too lazy to type it here. In fact, the solution was provided by my friend Noelene just one hour after I posted the riddle:

you put 3 coins on each side of the scale, leave two off

if they balance, then use your second weighing to compare the two you left off

if one of the sets of three is heavier, then compare two of the three coins with your second weighing

if they balance, then the third one is your counterfeit. if they [do not], then the heaver one is your counterfeit

but really, you should try and spend all eight coins as soon as possible and not worry about which one is fake

I like to cook, though I do not do it very often. I also like to bake. I think I would bake more if I had one of those scales and all my recipes measured ingredients in grams. Mass is much more precise — not to mention much more fun — than volume.

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?

I can only assume the first person with the correct answer was my father. He left enough clues to indicate he knew the solution, without reporting it directly or giving it away to anyone else. Very clever, Dad.

So, you want three numbers that multiply to get 72. Here are your options:

• 2 2 18
• 2 3 12
• 2 4 9
• 2 6 6
• 3 3 8
• 3 4 6

Update: As Clint pointed out in the comments, there are several more possibilities at this point. I completely left out the cases where one or more daughters are 1 year old. Which is silly of me, because I have nieces and nephews that are 1 year old. I think.

Thankfully, this oversight does not influence the outcome of the riddle.

A few loyal riddlers got to this point and gave me some mouth about needing to know the house number. But you really do not need to know the number. You go look at the house number, but it does not help. But it does! Knowing that the house number does not help actually helps, because now you can narrow your choices down to sets that have the same sum:

• 2 6 6
• 3 3 8

So what does strawberry shortcake have to do with all of this? Answer: nothing. The last piece of important information is the existence of one oldest child. Therefore, the ages must be 3, 3, and 8.

In England, house numbering starts at one end of the street at 1 and continues down one side in numerical order (2, 3, 4, …), then crosses the street and comes back down to the beginning. Therefore, the lowest- and highest-numbered houses are directly across from each other, and there is no “even side” of the street.

I hope you like math. All you need is math, and maybe a bit of patience to work it out, and this riddle is in the bag.

I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were.

“The product of their ages is 72,” he answered.

Quizzically, I asked, “Is there anything else you can tell me?”

“Yes,” he replied, “the sum of their ages is equal to the number of my house.”

I stepped outside to see what the house number was. Upon returning inside, I said to my host, “I’m sorry, but I still can’t figure out their ages.”

He responded apologetically, “I’m sorry. I forgot to mention that my oldest daughter likes strawberry shortcake.”

With this information, I was able to determine all of their ages. How old is each daughter?

I could really go for some strawberry shortcake myself right now. In fact, Rebecca and I are planning a trip to Sweet Berry Farm very soon, so that strawberry shortcake just might happen.

As many, many, many of my friends and family pointed out, the only way to correctly label the jellybean boxes is to take a single bean from the box labeled “Blue & Red Jellybeans.”

This one was too easy; my cousin Benjamin submitted the correct answer about two hours after the riddle was posted. This was followed by a flood of correct answers and “Did I win?” queries.

Ben, I owe you a box of jellybeans.