The goal of Yodoku is to place consecutive integers 1, 2, 3, … so that the numbers in each row and the numbers in each column are always increasing. This means that the player needs to compare and order non-consecutive numbers, in a few different lists simultaneously. This is a fun challenge for young mathematicians around ages 5 to 8.

Get started now with a printable set of Yodoku puzzles :

(Standards: Yodoku addresses kindergarten Common Core Standard CCSS.MATH.CONTENT.K.CC.C.7 / compare two numbers between 1 and 10 presented as written numerals.)

## Asking Good Questions

When completed, the Yodoku diagrams are examples of *Young tableaux*. A Young tableau is “a combinatorial object useful in representation theory and Schubert calculus” (Wikipedia). Combinatorics is the mathematics of counting things. It is fun to count things! So now I am wondering: “How many Young tableaux with five boxes are there?”

First, you need to count the number of Young diagrams. Young diagrams are just Young tableaux without the numbers. The rows must (1) line up on the left and (2) not increase in length. You can set up a nice investigation with snap cubes.

Here are two special shapes I made with 5 snap cubes. The rows don’t get bigger, and they line up on the left side. I wonder how many other shapes can make like that?

[It is helpful to move over the cubes to illustrate the non-examples.]

Then you might want to just keep counting Young tableaux. You could investigate the sequence counting the Young tableaux with size 1, 2, 3, 4, …

Or you might start filling in your shapes with numbers to find all the Young diagrams of a certain size.

Look, I filled in numbers from 1 to 5 so that each row is increasing and each column is increasing. I wonder how many other ways we can do that?

Can you (or, even better, you and a little one) find all the Young diagrams with 5 boxes? Happy counting!