Sudoku for Kids - Page 3
Lesson 4 - Hidden in Plain Sight
First, the answer to the homework question. You will remember that I asked “Let’s say you find a row that has three empty squares, all with possibilities 1, 2 and 3. Could this help you remove possibilities from other squares in the row?”
The answer is yes - and it works just like a locked pair. If you have three squares, each of which can be 1,2 or 3, then one of them has to be the 1, one of them the 2, and the other one the 3. So no other squares in the row could be a 1, 2 or 3. This is called a locked triplet. And if you guessed that you can have locked quads too, you’re right! But locked triplets and quads are very rare.
Okay, enough homework! Let's go to your next challenge!
Now the puzzles are getting really tough. You won’t find any forces, pins, or locked pairs at this point!
How can you possibly proceed? The key is that there is something very special about column 9. Can you see what it is? It’s sort of like a locked pair, but not quite the same.
Look at R4C9 and R5C9. What do they have in common that no other squares in column 9 share?
Both R4C9 and R5C9 have possibilities 1 and 5, and no other squares in column 9 can be a 1 or a 5. So that means one of the squares has to be a 1, and the other one has to be a 5. This is called a hidden pair because it is hiding inside a bunch of other numbers.
So now that you know that the 1 and the 5 must go in R4C9 and R5C9, that means that all their other possibilities - the 2, 3 and 9 - can be removed. This is called possibility reduction.
Many players call this a hidden locked pair, because once you’ve done the possibility reduction, you are left with a locked pair.
Once you’ve found this possibility reduction, the rest of the puzzle is easy; just a couple of pins and a lot of forces. Enjoy!
Lesson 5 - Ice Cream & Chocolate Cake
This puzzle will drive you crazy if you don’t know the secret of Intersections. There’s something special about row 1 and block 1 that lets you make progress. Can you figure it out all by yourself?
If you haven’t figured it out, here are some more clues. Your teacher may have already taught you about sets and intersections, but in case she hasn’t, or you need a reminder, this diagram might help:
Lets say the red circle represents all the kids in your class who like ice cream, and the green circle represents all the kids in your class who like chocolate cake. These are called sets.
What’s that, you say? Some of the kids like both ice-cream and chocolate cake? Well, I’m not surprised. I do too! In fact, I like ice-cream on my chocolate cake, and even ice-cream in my chocolate cake. Yuuuuuum! Fortunately, we can redraw the circles to show this.
Now the yellow area represents all the kids who like both ice-cream and chocolate cake! That’s called a set intersection.
Now lets look at the puzzle again, and at the intersection of row 1 and block 1
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Look at the yellow squares. They are in both row 1 and block 1; that means they are in the intersection of row 1 and block 1.
So how can this help us? Well, it’s super-tricky. If you’ve already figured it out, then I think you deserve both chocolate cake and ice-cream!
Look at row 1 again. Notice that the only place to put a 6 in row 1 is in one of the yellow squares. Either R1C2 or R1C3 must be a 6.
But these squares are also part of block 1, because they’re in the intersection. This means that the 6 in block 1 must also be in R1C2 or R1C3. And that means you can’t have a 6 in the other (red) squares of block 1!
Isn’t that cool? I’ll bet when you first learned about sets and intersections you thought they weren’t much use. And now you’ve learned that they can be used in a fun way.
It makes you wonder if some of those other boring math facts your teacher wants you to remember might have fun uses, doesn’t it?
Now go back to the original puzzle. Can you find other intersections in it? Believe it or not, there are 4 other useful intersections in the puzzle.
Can you find all found? I’ll tell you where they are later, but if you can find them, write them down here. One is really hard to find!
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Don't Cheat Now
Well, how many did you find? All four? Great!
Here are the answers:
The intersection of column 1 and block 4 is the only part of column 1 that can contain a 6. So you can remove 6’s from the rest of block 4.
The intersection of block 2 and row 2 is the only part of block 2 that can contain a 5. So you can remove 5’s from the rest of row 2.
The intersection of row 3 and block 3 is the only part of the row that can contain a 5. So you can remove 5’s from the rest of block 3.
and here’s the hard-to-find one:
The intersection of block 3 and row 3 is the only part of block 3 that can contain a 6. So you can remove 6’s from the rest of row 3.
Isn’t that interesting? The same intersection actually generated two different reductions! Also, did you notice that when you’re looking for intersections, you don’t just compare the rows and columns against the blocks, but also the blocks against the rows and columns.
Here’s my method for finding intersections: I look at each block, and divide it up into 3 rows of 3 squares. Then:
- If a possibility only appears in those squares and not in the rest of the row, I can eliminate it from the block.
- If a possibility appears only in those squares and not in the rest of the block, I can eliminate it from the row.
Then, I look at each block again, and divide it up into 3 columns of 3 squares. Then:
- If a possibility only appears in those squares and not in the rest of the column, I can eliminate it from the block.
- If a possibility appears only in those squares and not in the rest of the block, I can eliminate it from the column.
Whew! Bet that got your brain all over-heated. You need to cool it down. I suggest you eat some ice-cream!
Yuuuuuummmm! Iceeee-creeaaaaam! I think I deserve some for writing this lesson!
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