Problem 1. How many animals are there in the picture to the right? Let's begin by counting the animals there are in this picture. The first object we come across is a carrot. We know that that is not an animal. The second object is a dog. So we know that there's one animal. The next is a kangaroo. So that's two animals. And then the kangaroo has a baby, so that's three animals. This next object is a flower, and we know that's not an animal. The next one is a horse, so that's four animals. This apple is not an animal. And then finally we have a cat, which is an animal. So all together, we have one, two, three, four, five animals. So the correct answer is C. Problem 2. Which piece fits in the empty place in the puzzle on the right? Now to figure out which piece will fit into this puzzle, let's draw the piece that we think will fit. It has a straight line here, a straight line here, a bump out here, and a bump in there. Now let's take what we've just learned and apply it to every single piece that we see. This piece has a straight line, and a straight line, and a bump out, and another bump out. So we know that that's incorrect. And then here, we know that this is a straight line, and a straight line, and a bump out, and a bump in. So this is looking pretty good, but let's check it with everything else. Because this piece has a straight line, and a straight line, and a bump out, and a bump in, so that could look okay too. This piece has three straight lines, and so that's out automatically. And this piece has a straight line, and a straight line, and a bump in, and a bump in. So we know that that piece is incorrect as well. So now we have to make up our mind between B and C. Now let's take a look at this. Now let's redraw both B and C so that they're rotated in the same way that they are in this puzzle. So let's redraw piece C. It has two straight lines here, and then it has a very gentle curve here, and a very steep curve like this here. Now if we compare that to the piece in the puzzle, we can see that that's wrong. And then just to be safe, let's try to redraw piece B. So we have a straight line, a straight line, a gentle curve here, and a gentle curve here, and then we see that yes, B is the correct answer. Problem 3. How many legs do these animals have all together? So let's figure out how many legs these five animals have all put together. So let's write down how many legs each animal has. This chicken has one, two, two legs. This cat has one, two, three, four legs. This chicken has one, two, two legs. This one, again, one, two, two legs. And then this dog has one, two, three, four legs. And now let's add them together. That's equal to fourteen. And so the correct answer is D. Problem 4. Helena wrote the word kangaroo twice. How many times did she write the letter A? To solve this problem, let's write the word kangaroo twice and then count how many times we write the letter A. Here's kangaroo once. And then let's write it again. Kangaroo. Kangaroo. Now let's count how many times the letter A has been written. That's one, two, three, and four. The letter A has been written four times. The answer is D. Problem 5. Luke repeats the same four stickers on a strip. Which is the tenth sticker put down by Luke? To solve this problem, let's figure out the pattern that already exists within these stickers. We know that the first sticker is a penguin. And then a frog. And then a teddy bear. And then a dinosaur. And then we see a penguin again. Since we know that there are four stickers and that they repeat, it makes sense that if it's a penguin, the pattern starts to repeat. Penguin, frog, teddy bear, dinosaur. And that's again four stickers, so now the pattern repeats. So the next sticker should be a penguin. And then the sticker after that, the sticker that we are looking for, is going to be a frog. And so the correct answer is B. Problem 6. On Friday, Dan starts to paint the word banana. Each day he paints one letter. On what day will he paint the last letter? So let's begin by trying to understand what's going on in this problem. On Friday, Dan starts to paint the word banana. Each day he paints one letter. So let's try to draw that out. On Friday, Dan paints the letter B. On Saturday, he'll paint the letter A. On Sunday, he'll paint the letter N. On Monday, he'll paint the letter A. On Tuesday, he'll paint the letter N. And on Wednesday, he'll paint the letter A. So on what day will he paint the last letter? Well, we've just figured it out. It's on Wednesday, and so the correct answer is C. Problem 7. Which of the bolded paths is the longest? We want to figure out which of the following paths is the longest. Now since each of these paths is drawn on graph paper, it's pretty easy. All we have to do is count the number of sides that each path has. So here it's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Path A is 13 grid lengths long. Now let's count the length of path B. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Path B is also 13 grid lengths long. Now let's count path length C. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Path C is also 13 lengths long. Now let's count path D. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Path D is 13 grid lengths long. Now let's count the path of the last one of E. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Path E is 15 lengths long. And so we know that E is the correct answer. Problem 8. Katya is in a boat on a lake. Which of the pictures does she see in the lake? This question is asking what Katya will see reflected in the lake. Now let's begin by trying to draw what she will see. Everything will be reflected symmetrically along the line of the seashore. The trunk of the tree is closest to the shore of the lake so that it will be reflected first. And then after it, you will see reflected the rest of the tree, like this. It is symmetrical to this axis right here of the shore. Now the moon is next. It will be located, again, symmetrically. And since it's at the top of the tree on this side of the lake, reflected in the lake, it will also be on the top, towards the top of the tree, and it will be reflected in the same way. And so the picture that we've just drawn is picture number C. So that is the correct answer. Problem 9. Thirteen children are playing hide and seek. One of them is the seeker. After a while, nine children have been found. How many children are still hiding? So thirteen children are playing hide and seek. One of them is the seeker. That means that if you subtract that one child from the thirteen that are playing, you get twelve children who are hiding. If after a while, nine children have been found, you subtract nine children who have been found from the twelve that are hiding, and you get three children that are still left and who are still hiding. So the answer is A. Problem 10. Father hangs the laundry outside on a clothesline. He wants to use as few pins as possible. For three towels, he needs four pins, as shown. How many pins does he need for nine towels? To solve this problem, let's continue drawing the towels as the father continues to hang them. So he's hung three towels already, and now he hangs the fourth. And this pin here holds on to these two towels, and then you add another pin here. And then you draw another towel and another pin, and so now we have five towels. Now we have six. Seven towels. Eight. And nine. And so let's try to count the number of pins that we are using. One, two, three, four, five, six, seven, eight, nine, and ten. So the correct answer is B. Problem 11. Today, Betty added her age and her sister's age and got ten. What will the sum of their ages be one year from today? We know that Betty's age plus her sister's age is equal to ten years. And we know that one year from now, Betty will be one year older, and her sister will be one year older, so that in one year, the sum of their ages is going to be twelve. So the correct answer is D. Problem 12. The clock shows the time when Stephen leaves school. Lunch at school starts three hours before school ends. At what time does lunch start? The clock shows the time when Stephen leaves school. The small hour arrow is pointing to two o'clock. And we know that lunch at school starts three hours before school ends. So to find out what time lunch starts, we have to count backwards. One hour, two hours, three hours to eleven o'clock. So lunch starts at eleven at Stephen's school. The answer is D.

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