1. If your school has not checked in, please send one student and one adult to the registration table at the front of the Activity Center. Schedule 8:00 – 8:30 Check-In 8:30 – 8:45 Greeting from the Principal 8:45 – 9:15 Math Medley Exam 9:15 – 9:30 Break 9:30 – 10:00 Individual Subject Competition 10:00 – 10:15 Break 10:15 – 11:45 Super Quiz Bowl and Solutions 11:45 – 12:00 Results and Awards

2. This is a group competition in which many problems must be solved through collaboration. Scratch paper is available at your tables, but the final answer for each problem must be written legibly in the box on the provided answer forms. The final solution must be true for all the given clues. Each question is worth different amounts of points based off of the complexity, but partial points may be awarded on some problems.

3. +9+=20 +x ÷ x+=15 +x+ +4–6=3 === 7214  Numbers 1- 9 are filled in to make the rows and columns equal the value indicated using the given operations. Numbers 4, 6, and 9 have been filled in. Fill in the remaining values: 8 1, 2, 3, 5, 7, 8

4. +9+=20 +x ÷ x+=15 +x+ +4–6=3 === 7214 5 2 8 1 7 3

6. 24’ 4’ 2’ ●A●A ●B●B ●C●C ●D●D ●E●E ●F●F ●G●G ●H●H 16’ 32’ 48’ 24’ 8’ 4’ 2’ 8’ 2’ 30

7. Guess Number Correct Places Correct 6200 3110 7510 4711 1722  I’m thinking of a 2-digit number.  The number does not begin with a 0 and none of the digits in the number are the same. (ex: 77 is not allowed).  If you guess what my number is, I’ll tell you if any of the numbers in it are correct, and then I’ll tell you if any of them are in the correct place.  We can play this game with any size number. Correct Answer

8.  Guess the numbers based on the information given in each table. Remember, no number begins with 0 and no number has digits that repeat. Problem AProblem BProblem C Guess a two digit numberGuess a three digit number Guess Number Correct Places Correct 2400 1410 8611 Guess Number Correct Places Correct 15300 98211 53211 47120 Guess Number Correct Places Correct 31010 63020 73511

9. 7 6 0 472 81  Each clue tells us something about our number YX BAC ML N If 6 & 0  _06 or 06_ If 6 & 3  _63 Guess Number Correct Places Correct 31010 63020 73511 Problem AProblem BProblem C Guess a two digit numberGuess a three digit number Guess Number Correct Places Correct 2400 1410 8611 Guess Number Correct Places Correct 15300 98211 53211 47120

10.  If you re-assemble the pieces of the four compositions below by moving pieces, rotating pieces, or flipping pieces, three of them will be the same shape, and one will not. Which is the odd one out? What shape is formed with the other three?

11.  A, C, and D can be re-assemble each to form a square. B can not be re-assembled to become a square.

12.  Quento is a game played on a 3x3 grid with 5 numbers and four operations. Players draw line segments that connect a designated number of values and any arithmetic operations between them to create target values  For instance, if your goal was to create the number 7 with two numbers, you could use either the 4 + 3 combination or the 8 – 1 combination 4+8 +3– 2+1 4+8 +3– 2+1

13.  If your goal was to create the number 6 with a three number combination, you could use 4 + 3 – 1 or 8 – 3 + 1 or even a clever use of negative signs, like -1 + 3 + 4.  Keep in mind that order matters. 8 – 3 is not equal to 3 – 8. Since order matters, you need to indicate the direction that you travel. 4+8 +3– 2+1 4+8 +3– 2+1 4+8 +3– 2+1

14.  Today’s Grid + Goals a) Use two numbers to create 11 b) Use two numbers to create 3 c) Use three numbers to create 9 d) Use three numbers to create 7 e) Use three numbers to create –9 f) Use four numbers to create –9 g) Use four numbers to create 17 h) Use four numbers to create 8 i) Use five numbers to create 12 1+4 –8– 6+5

15.  Answers can vary and still be correct. This shows just one solution for each. 1+4 –8 6+ Two numbers to create 11Two numbers to create 3Three numbers to create 9 Three numbers to create 7Three numbers to create –9Four numbers to create –9 Four numbers to create 17Four numbers to create 8Five numbers to create 12 1+ –8– 65 1+4 –8– 6+5 –8 6+56+5 –8– 65 8– 5 1+4 –8– 6 1+4 –8– 6+5

16.  The game 6 NUMBERS allows players to use addition signs, subtraction signs, multiplication signs, division signs, (parentheses by grouping) and 6 numbers to write an expression equivalent to a target value. You do not need to use all the numbers, nor all the signs. Though you may repeat signs, but you may not use a number twice.

17.  Example: Create 106 from 2, 4, 3, 6, 10, and 100 Here are just some of the ways you can achieve your goal. You only need one. 100 + 6 = 106 100 + (2 x 3) = 106 (100 + 10) – (6 / 3) – (4 / 2) = 106 No number is used twice but signs can be repeated.

18.  Using addition signs, subtraction signs, multiplication signs, division signs, parentheses, and only the 6 numbers given in each set, write an expression equivalent to each target value. Remember, you do not need to use all the numbers or all the signs. You can repeat signs, but you may not use a number twice. GoalNumbers 2101, 2, 4, 10, 25, 100 1173, 4, 9, 10, 25, 50 2301, 2, 8, 10, 75, 100 3873, 4, 5, 12, 50, 100 9451, 2, 8, 9, 50, 100

19.  This is just one solution. Others may be possible. GoalNumbersOne Solution 2101, 2, 4, 10, 25, 100(100 x 2) + 10 1173, 4, 9, 10, 25, 50(10 + 3) x 9 2301, 2, 8, 10, 75, 100(75 x 2) + (10 x 8) 3873, 4, 5, 12, 50, 100(100+ 5 + (6 x 4)) x 3 9451, 2, 8, 9, 50, 100(50+9) x (8 x 2) + 1

20.  In variations of the popular puzzle game, Sudoku, each row and column in an n x n square has the numbers 1 to n listed only once in each row and column. For example, on a 3 x 3 grid, the numbers 1, 2, & 3 are listed once in each row and once in each column. For instance. 132 213 321

21.  In Math Doku+ (also known as Ken-Ken), the same principal is true, except a layer of math is added onto it. Each colored grouping of numbers has an operation and a value in the upper left hand corner of that group. The goal is to use that operation with the numbers in that group to get that value. For instance: 8+ 2- 6x 1

22.  The Sum (addition) of the numbers in the red grouping is 8  The difference (subtraction) of the two numbers in the yellow group is 2 (here there’s no need for a negative)  The product (multiplication) of the numbers in the green group is 6  For this blue group, the number 1 goes inside.  Remember, each row and column has the numbers 1, 2 and 3 with no repeats. This can be played on square grids as large as you want. 132 213 321 8+ 2–2– 6x1

23.  Goal: Fill in the numbers missing from each grid. Using numbers 1, 2, and 3, fill in the 3 x 3 grid below. Using numbers 1, 2, and 3, fill in the 3 x 3 grid below Using numbers 1, 2, 3, and 4 fill in the 4 x 4 grid below Using numbers 1, 2, 3, 4, and 5 fill in the 5 x 5 grid below

24.  Use logic to find one piece, and fill in the rest as that piece eliminates other options Using numbers 1, 2, and 3, fill in the 3 x 3 grid below. Using numbers 1, 2, and 3, fill in the 3 x 3 grid below Using numbers 1, 2, 3, and 4 fill in the 4 x 4 grid below Using numbers 1, 2, 3, 4, and 5 fill in the 5 x 5 grid below 2 1 3 2 2 1 3 3 3 3 3 1 1 1 2 2 2 3 4 3 3 1 1 42 4 21 24 1 1 2 2 35 5 5 3 4 1 4 3 3 1 5 5 24 2 1 4 4 2

25.  How many non-congruent (different shaped) triangles can you create by connecting any three dots from the 3 by 3 grid of dots in the figure below. Draw each triangle in the grid provided. Please draw them smallest to largest (it helps with grading but doesn’t affect your score).  How many are right triangles? Example  How many are acute triangles? Example  How many are obtuse triangles? Example ●●● ●●● ●●●

26. ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● ●●● Increasing Areas Triangles with Area = ½ Triangles with Area = 1Triangles with Area = 2 8 total triangles: 4 are right (Yellow), 2 Acute (light green), 2 Obtuse (dark green)  Be organized. A triangle has 3 points. Start with the 1 st point, pick the 2 nd, then pick all possible 3 rd points.

27.  Another Classic Riddle: Take half of this, and add one more Then treble that, and add on four. But just the same result you’d see by adding this to twenty three. So what is this? You’ll have to say! Your fun with figures for today.  Find what number represents This  Hint: “Treble” means multiple by 3

28. Take half of this, and add one more Then triple that, and add on four. But just the same result you’d see by adding this to twenty three.

29.  A classic riddle “My age?” She smiled. “You’ll have to guess. Just let me think. Ah that’s it yes. Reverse my age: divide by three: add thirty-four. My age you’ll see.” That’s what she said. So can you say how old she must have been that day?  Determine the woman’s age in the poem. Hint: She’s Double Digits Years old!

30. 24 24 24/3 8 + 34 24 Her Age “Reverse my age“ “divide by three” “add thirty-four” “My age.” YX YX (YX)/3 [(YX)/3] + 34 YX

31.  The number 80 is the sum of four positive numbers a, b, c, d such that a increased by 4, b decreased by 4, c multiplied by 4, and d divided by 4 all equal the same number.  Determine what this same number is (hint: it is a decimal)  2 Points for finding 2 consecutive positive integers that the number is trapped between.  2 Points for finding the number  3 Points for finding the values of a, b, c, and d.

32. Problem is based on Question by Ellicott Geographer General Divide 60 into four Such parts, that the first being increased by 4, the Second decreased by 4, the third multiplyed by 4, the fourth part divided by 4, that the Sum, the difference, the product, and the Quotient shall be one and the Same Number. Using the Single Position method, guess at the "same number." Let's guess 16. Then the first part is 12 (12 + 4 = 16), the second part is 20 (20 - 4 = 16), the third part is 4 (4 x 4 = 16), and the fourth part is 64 (64 / 4 = 16). These four parts add up to 12 + 20 + 4 + 64 = 100. Therefore, the correction factor is 60/100, or 3/5. Thus the answer is the guess, 16, times the correction factor, 3/5; 9.6 is the value for the "same number." The four parts, then, are 5.6, 13.6, 2.4, and 38.4 -- their sum to 60, the desired result. Single Position works here because, since the guess produced too large a result, it is reduced by a correction factor based on the ratio of the desired answer to the incorrect answer.

33. Problem is based on Question by Ellicott Geographer General Divide 60 into four Such parts, that the first being increased by 4, the Second decreased by 4, the third multiplyed by 4, the fourth part divided by 4, that the Sum, the difference, the product, and the Quotient shall be one and the Same Number. Using the Single Position method, guess at the "same number." Let's guess 16. Then the first part is 12 (12 + 4 = 16), the second part is 20 (20 - 4 = 16), the third part is 4 (4 x 4 = 16), and the fourth part is 64 (64 / 4 = 16). These four parts add up to 12 + 20 + 4 + 64 = 100. Therefore, the correction factor is 60/100, or 3/5. Thus the answer is the guess, 16, times the correction factor, 3/5; 9.6 is the value for the "same number." The four parts, then, are 5.6, 13.6, 2.4, and 38.4 -- their sum to 60, the desired result. Single Position works here because, since the guess produced too large a result, it is reduced by a correction factor based on the ratio of the desired answer to the incorrect answer.

34. Students Ambassadors AP Calculus Students Members of Math Department Parents, Teachers, and Principals Participants

35. Many of these problems, as past problems from math Competitions, were inspired by apps from smart phones. If you’re going play on your phone, play smart! NineGaps 6 Numbers Math Doku+ Quento

36. #TypeProblemTime Work (in min) Time Explain (in min) ScoringTotal Points total Presenter 1AL9 Gaps Square311 solution (1pt - 1 st, 1pt - 2 nd, 2pts- rest)4 points 2GMidpoint321 solution (only one solution)5 points 3ArMaster Mind433pts / problem (X 3 problems)9 points 4LRTetris211 solution (2 solutions) 2 points each4 points 5ArQuento421pt / problem X (9 problems)9 points 6AL6 Numbers422 pts / problem (X 5 problems)10 points 7ArMath-Doku522 pts / problem (x 4 problems)8 points 8GTriangles431pt / triangle (X 7 triangles) +1 #right Δ, +1 #Acute Δ, +1 Obtuse Δ 10 points 9ALWhat is This421 solution (5 points)5 points 10ALClose Secret421 solution (5 points)5 points 11LRNumber in 4 Parts53+2 pts trap, +2 pts value, 3pts a, b, c, d7 points 42 min.23 min.76 points