Professor Layton ambled through the main quadrangle of Gressenheller University, a grassy yard with which he was highly familiar. A few students and faculty were walking around, and a group of the university's day-care children were sitting in a circle, playing a game.
No suspects here, he thought, so why do I feel like I'm being followed?
On instinct, Layton turned around to find a small mallard waddling towards him, proudly carrying a piece of bread in its bill.
How curious. Is this duck perhaps acquainted with me?
The mallard dropped its prize at Layton's feet. Layton stooped down to examine it. What he had thought was a piece of bread was revealed to be a small sheet of paper with writing on it. A puzzle?
"Sir, is this for me?"
"QUACK." The mallard flapped its wings and used its bill to nudge the paper closer to Layton.
"I see. Well, thank you, sir." Slightly unsettled, Layton began to read the text on the page.

It’s recess time! Some students decide to play a fun playground game. The rules of the game are:

One student is It, and stands while the others sit in a circle facing the center. The It walks counterclockwise around the outside of the circle and taps students in turn, calling each a Buck until finally calling one a Moose. The Moose then gets up and tries to tag the It, while the It runs counterclockwise around the circle to return and sit where the Moose had previously been sitting.

If the It successfully claims the empty seat, the Moose becomes the new It. But if the Moose tags the It before they can sit, then the Moose returns to their seat and the It begins the process again. In this game, the It will always outrun the Moose and take their seat unless otherwise specified. The first It can begin anywhere around the circle, though the first student tapped on subsequent turns will always be the one sitting counterclockwise from the location where the most recent Moose was seated.

The playground monitor challenges each student to keep track of the total number of heads that they tap during the game. But they aren’t very good at following instructions...

List of Students

Angus (male): After tapping 3 Bucks, he will then select the next boy as Moose.

Daisy (female): Wears a pink bow. She will tap as many Bucks as the number of times she’s It.

Daphne (female): Wears a yellow hat. She has a bad memory and will only keep track of the count from her most recent turn as It.

Dewey (male): Brother of Huey and Louie. If any of the brothers have been It before, he will tap one more student than the last brother who was It.

Donald (male): Wears a blue cap.

Gus (male).

Huey (male): Brother of Dewey and Louie. If any of the brothers have been It before, he will tap one more student than the last brother who was It.

Louie (male): Brother of Dewey and Huey. If any of the brothers have been It before, he will tap one more student than the last brother who was It.

Lucky (???).

Matilda (female): To keep numbers simple, if her Buck/Moose count grows to double digits, she will drop the digit in the tens place.

Melissa (female): Only counts every other student tapped.

Molly (female): Will only report the digit in the tens place when asked.

Tanya (female): Wears a purple bandana. After tapping 5 Bucks, she will then select the next girl as Moose.

To begin, the students all draw numbers and sit in clockwise ascending order. The student who drew #1 decides that will be their special number for the game and as such, they will always tap the first student as Moose when they are It. The student who drew #13 becomes the first It and remains standing.

The seated students, clockwise from Angus, are:

Angus, Dewey, Molly, Gus, Huey, Louie, Daphne, Donald, Matilda, Lucky, Tanya, and Daisy.

Progression of the Game

The It begins by tapping a student sharing their same initial, and taps a total of 2 girls and 2 boys - including one with a head accessory - before taking off at a run and making it safely to a seat in the circle.

The It walks past a student also wearing a head accessory and taps the next person as the Moose.

Element of surprise! The It immediately taps the next student as the Moose and successfully runs a lap.

The It swipes Donald’s cap as she yells “Moose!” and runs away. She drops the cap on Melissa’s head on the way around. (Gross, cooties! Melissa tosses the cap at the nearest boy.)

Donald taps a Moose, runs around, and claims a seat.

The It calls out “Buck, Buck, Moose” and outruns his brother around the circle.

The It chooses another Moose and also sits back down.

The It takes their turn, while the two closest seated students with head accessories decide to exchange them.

Daphne notices the brothers are evenly spaced around the circle, and decides to change that up by tapping the closest one and making him move.

As the next two Its take one turn each, another pair of head accessories are swapped between neighboring students in the circle.

The It taps Molly as Moose, but she quickly tags him back. Fine! He decides to choose a student that he’d previously outrun. It’s successful, and he decides not to count his failed attempt towards his Buck/Moose total.

The It walks halfway around the circle to tap Matilda, who then taps and outruns the student wearing the blue cap.

The It walks two-thirds of the way around the ring, before tapping someone else and claiming their spot.

The It sees three head accessories in a row, and taps the student wearing the last of these to be the Moose.

The It taps someone with the same length name and sits back down in their starting location. Nice! Meanwhile, Donald tries to get his cap back from the student next to him - but she plays keepaway and passes it to the student on her other side.

Louie walks past both his brothers - then runs past both of them - before also sitting back down in his original spot. The student he ousted then walks around and taps everyone in the circle, before tapping and outrunning the only student who had never before been It.

The It taps someone else as Moose and sits down, noticing that the head accessories are now evenly spaced around the circle.

The It taps double the number of heads as their previous turn, before sitting back down.

The It returns to a more traditional game count and chooses a nearby student as Moose.

The It, having reset their total count to 0, walks nearly all the way around before tapping and outrunning a student with the same length name.

The It passes two accessorized students before tapping one of the brothers as Moose - who again one-ups his last sibling’s count.

Lucky, turned It by one brother, taps the next closest in turn and finds a seat. Ousted from his spot, the It chooses a new Moose and sits back down next to his brother.

The It decides to tap as many heads as their starting position, and outruns the Moose to take their spot.

The It passes by all three brothers, before choosing the first of five girls in a row to be Moose.

The It shouts “Moose!” while tapping the yellow hat. As the two students chase each other, another slides over to the empty space to give the Moose more time to catch up - but to no avail.

After clarifying the rules, the It considers turning the tables on the previous It, but continues on to tap the first and only boy she’s passed all game - and as she claims his spot...

Riiing! Recess is over! The It storms off in a huff, as the playground monitor approaches and asks the students to report their counts in clockwise order, starting with Donald.

Hint 1:
Lucky is female.
Hint 2:
When the head accessories are evenly spaced around the circle, the students wearing them are Gus, Angus, Daphne, and Daisy.
Hint 3:
Clockwise from Donald, the final order of students is: Donald, Matilda, Angus, Dewey, Daisy, Daphne, Molly, Lucky, Melissa, Tanya, Louie, and Huey.