Looking for today's Connections answer for puzzle #401 on July 156, a little harder than yesterday's answer, this puzzle from Connections Companion has a difficulty rating of 2.6 out of 5.

We update our Connections clues and hints daily. And if the hints aren't enough, you can see all four solutions along with the category title and related words. In addition, for those of you reading this in a different time zone, I have included a reflection on yesterday's puzzle #400.

There are spoilers for Connection 401. Only those who want to know the answer to today's Connections should read on.

Alternatively, see our NYT Connections How to Play Guide for tips on how to solve the puzzle without our help.

While today's Wordle solution guide recommends the starting word in Wordle as the strategy, the Connections solution requires you to identify the categories that are connected from the 16 words. The difficulty of each category is represented by a color, with yellow being the easiest grouping and purple the most difficult. Hints will help as the answer is displayed after four wrong guesses.

If you need a hint to solve the groupings, here are each theme in order of difficulty:

If you read these hints, you should at least find the answer to today's connection. If not, please continue reading for larger hints. Also, if you only want to know the answer, scroll down further.

There is an even bigger clue. Don't start today's puzzle in a grumpy, sing-songy mood, and consider all the possible forms Peter could take, even though you may not be able to guess.

Now for the answer to the 401st connection.

Drum roll please.

We continue to get the purple category first, and should continue to do so today.

I actually had Pan, Parker, and Rabbit, but for some reason it never occurred to me that Piper was Peter. Especially since I spent many a birthday party at the Chuck E. Cheese version of Peter Piper Pizza in San Antonio. There seem to be a lot of them in Arizona, but the only one I remember is in Texas. After all, I was the last one to eat Purple.

So yellow was actually the first category. Testy and Cross were easy to find from there.

The grid was down so that pilots, spares, and trials were nearby. From there it was just a matter of finding something that would lead to exploration.

To be honest, Broadway musicals are not my thing. I chose this one because it didn't fit in with “The Three Peters.”

It was not my best day.

I'm reading this late in the day. According to Connections Companion, the difficulty level was 2.4 out of 5.

For the second day in a row, I now feel like a damned genius because I guessed the purple category on the first try.

Then came the yellow, which could have been more troublesome if the Connections staff had thrown in a little more red string: Believe and Trust are similar enough to stay on the right path, and Accept （Accept” and ‘Buy’ are the only clues that even seem synonymous.

I admit that I stumbled in solving the blue category; I got as far as connecting Bracket, Mount, and Stand, but for some reason Base didn't click until my second or third attempt.

The hints “bluff” and “show” got me thinking about poker.