Occasional Puzzles - 🍎 Food Groups
Today's puzzle is inspired by the New York Times's Connections, which debuted last year and quickly became one of our favorite NYT games.
Here, we try to take the concept one step further by giving the whole puzzle a unifying theme (plus we think this one is slightly harder than your average New York Times Connections puzzle).
Today's Puzzle - 🍎 Food Groups
In the grid below, find four sets of four words that have something in common.
Here are some examples (unrelated to the puzzle below):
- BLUEBERRY, CHERRY, APPLE, PECAN → flavors of pie
- KISS, CROSS, CHI, TEN → represented as 'X'
- TRY, APPLICATION, RULED, ESSAY → words that follow 'college'
The puzzle contains exactly four sets of four, and each word is only used once. If you find a set of five, one of the words actually belongs to another set!
Source: Giphy
Previous Puzzle - 💝 Truffle Trials
Puzzle
Happy Valentine's Day! This year, your dear partner has thoughtfully (and diabolically) presented you with a box of nine chocolate truffles.
From the outside, all nine truffles look identical. But, on the inside, two of the truffles are filled with licorice cream (ew). Fortunately, you know the licorice truffles weigh slightly more than the pure chocolate ones.
You don't have a digital scale, but you do have an old-fashioned balance. It's the kind with two plates, which tells you which side is heavier but doesn't provide any numeric values.
Using just four weighings* on the balance, can you figure out which two truffles to avoid?
*One weighing means one fixed weighing. No incrementally adding or taking away truffles to see how the weight changes.
Solution [SPOILER]
We were really struggling to express this solution concisely, until Steve in Mountain View sent us an excellent writeup of his thought process, on which this explanation is based. Thank you, Steve!
The key to this puzzle is to first divide the 9 truffles into 3 groups of 3, then weigh those groups against each other. Let's call these groups A, B, and C.
For the first weighing, we'll weigh A against B. Then, for the second, we'll weigh B against C. The results of these two weighings tell us which groups the heavy (and therefore gross) truffles are in. There are 6* possible outcomes:
- A = B and B > C: this means that A and B are both heavier than C, so A and B must each have one licorice truffle.
- A = B and B < C: this means C is heavier than both A and B, so C must have both licorice truffles.
- A > B and B = C: this means A is heavier than both B and C, so A must have both licorice truffles.
- A > B and B < C: this means A and C are both heavier than B, so A and C must each have one licorice truffle.
- A < B and B = C: this means B and C are both heavier than A, so B and C must each have one licorice truffle.
- A < B and B > C: this means B is heavier than both A and C, so B must have both licorice truffles.
After the first two weighings, we have now identified the group (or groups) containing the licorice truffles. All that's left is to determine, within a given group, which truffle is which.
If the licorice truffles are in the same group, then you simply take any two truffles from that group and weigh them against each other. If they're the same, they're both licorice. If one is heavier, it's licorice, along with the remaining unweighed truffle. So now you've found both licorice truffles! Total weighings? Three.
If, on the other hand, the licorice truffles are in different groups, you'll need to use the fourth weighing. As a reminder, you know that each of these groups of 3 contains exactly 1 licorice truffle. First, take one of the groups and weigh any two truffles against each other. If they're different, the heavier one is the licorice truffle. If they're the same, then neither is licorice, and the unweighed truffle is. Now, just do the same thing with the other group! Total weighings? Four.
* Astute readers may note that, since there are three possible outcomes of each weighing, there should be 3*3=9 possible outcomes from the first two weighings. However, 3 of them are impossible based on the setup of the puzzle. We'll leave it to you to figure out why 😊