#### A Math Forum Project

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For many years mathematicians, scientists, engineers and others interested in mathematics have played year games via email and in newsgroups. We don't know if it is possible to write expressions for all the digits from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find.

As with many games, the rules for the Year Game may vary slightly. This web page is intended for students in grades three through twelve with a general knowledge of mathematics.

Use the digits in the year 1998 and the operations of +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100. Please read the rules carefully if you wish to have your solutions posted.

Print a worksheet for your students to record their findings. Or, print a sheet of manipulatives for your students to use.

Send student solutions to Judy Ann Brown Check the full list of student solutions.

## STUDENT SOLUTIONS

 Solution Name Grade School 1 (sqrt(9)+8)-(9+1) Stoy group 2 5 Stoy School Westmont NJ 2 (9+9)÷(8+1) Eric Todd 8 Nichols Middle School Buffalo, NY 3 sqrt(9-9+8+1) William Simpson 6 Newark Boys Chorus School, Newark, NJ 4 (sqrt(9)+9)-(8x1) Stoy group 2 5 Stoy School Westmont NJ 5 sqrt[9+9+8-1] William Simpson 6 Newark Boys Chorus School, Newark, NJ 6 8-1-(9÷9) NBCS group 6 6 Newark Boys Chorus School Newark,NJ 7 9-9+8-1 Jesse Gray 5 Johnson Elementary School Richmond, VA 8 (1x8)+(9-9) Stoy group 5 5 Stoy School Westmont NJ 9 9+9-1-8 Rachel Huitt 11 Calamus-Wheatland Jr. Sr. High School Wheatland IA 10 9x1-8+9 Julia D'Rozario 5 Johnson Elementary School Richmond, VA 11 1+9+9-8 Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA 12 sqrt(9) + 9x1^8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 13 sqrt(9+8-1)+9 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School Wheatland, IA 14 sqrt(9)+sqrt(9)+8x1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 15 sqrt(9)+sqrt(9)+8+1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 16 8x(9÷9+1) NBCS group 7 7 Newark Boys Chorus School Newark,NJ 17 9!÷8!+(9-1) Stoy group 6 5 Stoy School Westmont NJ 18 9!÷8!+(9x1) Stoy group 6 5 Stoy School Westmont NJ 19 9!÷8!+(9+1) Stoy group 6 5 Stoy School Westmont NJ 20 sqrt(9)+9+8x1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 21 sqrt(9)+9+8+1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 22 sqrt(9)x8-(sqrt(9)-1) MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 23 (9÷sqrt(9)x8)-1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 24 9÷sqrt(9)x8x1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 25 (9+9)+8-1 NBCS group 6 6 Newark Boys Chorus School Newark,NJ 26 (9+8)+(9÷1 Stoy group 8 5 Stoy School Westmont NJ 27 1+9+9+8 Eric Todd 8 Nichols Middle School Buffalo, NY 28 9!÷8! x sqrt(9)+1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 29 sqrt(9)!xsqrt(9)!-8+1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 30 sqrt(9)x(9+1^8) MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 31 ((sqrt(9))!-1)x8-9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 32 (9-1)xsqrt(9)+8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 33 sqrt(9)x[8+sqrt(9)]x1 Vinnie Westphal 6 Mount Olive Middle School Budd Lake, NJ 34 9 x sqrt(9)+(8-1) NBCS group 8 8 Newark Boys Chorus School Newark,NJ 35 1x(9 x sqrt(9)+8) NBCS group 8 8 Newark Boys Chorus School Newark,NJ 36 9xsqrt(9)+8+1 Michael Lee 5 Johnson Elementary School Richmond, VA 37 (sqrt(9))!x(sqrt(9))!+1^8 Cheryl Morton 11 Norton High School Norton, MA 38 (9+1)xsqrt(9)+8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 39 (sqrt(9))!x8-9x1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 40 (sqrt(9))!x8+1-9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 41 8x(sqrt(9)+1)+9 Beth Affanato 11 Norton High School Norton, MA 42 (sqrt(9))!x8-(sqrt(9))!÷1) Casey Leavitt 11 Norton High School Norton, MA 43 (sqrt(9))!x(sqrt(9))!+8-1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 44 (sqrt(9))!x(sqrt(9))!+8x1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 45 (8-sqrt(9))x(9÷1) Casey Leavitt 11 Norton High School Norton, MA 46 9x(8-sqrt(9))+1 Cheryl Morton 11 Norton High School Norton, MA 47 [(sqrt(9)+sqrt(9))x8]-1 Stoy group 3 5 Stoy School Westmont NJ 48 [(sqrt(9)+sqrt(9))x8]x1 Stoy group 3 5 Stoy School Westmont NJ 49 8x(sqrt(9)+sqrt(9))+1 Katie Lank 11 Norton High School Norton, MA 50 (8-sqrt(9))x( 9+ 1) Katie Lank 11 Norton High School Norton, MA 51 sqrt(9)x(8+(9x1)) Cara Janczunski 11 Norton High School Norton, MA 52 (9+8)xsqrt(9)+1 Katie Lank 11 Norton High School Norton, MA 53 9x(sqrt9)!-1^8 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 54 9x(8-1)-9 NBCS group 7 7 Newark Boys Chorus School Newark,NJ 55 8x(9-1)-9 NBCS group 7 7 Newark Boys Chorus School Newark,NJ 56 (sqrt(9))!x8+9-1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 57 (sqrt(9))!x8+9x1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 58 (sqrt(9))!x8+1+9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 59 ((sqrt(9))!+1)x8+sqrt(9) Cheryl Morton 11 Norton High School Norton, MA 60 (8-1)x9-sqrt(9) Casey Leavitt 11 Norton High School Norton, MA 61 (sqrt(9))!x9+8-1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 62 (8x9)-9-1 Brittney Anderson 5 Johnson Elementary School Richmond, VA 63 (9x8)-(9x1) Stoy group 7 5 Stoy School Westmont NJ 64 [(9x8)+1]-9 Stoy group 7 5 Stoy School Westmont NJ 65 8x9-(sqrt(9)!+1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 66 9x(8-1)+sqrt(9) Casey Leavitt 11 Norton High School Norton, MA 67 8x(9-1)+sqrt(9) Beth Affanato 11 Norton High School Norton, MA 68 8x9-(sqrt(9)+1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 69 8x9-(sqrt(9))x1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 70 8x9-(sqrt(9) -1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 71 8x(9+1)-9 NBCS group 6 6 Newark Boys Chorus School Newark,NJ 72 9x9-1-8 Megan Gersch 5 Johnson Elementary School Richmond, VA 73 9x9x1-8 Kristen Marshall 5 Johnson Elementary School Richmond, VA 74 9x9-8+1 Zohaib Damani 5 Johnson Elementary School Richmond, VA 75 sqrt(9)+8x9^1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 76 9x8+sqrt(9)+1 Katie Lank 11 Norton High School Norton, MA 77 (9+1)x8-sqrt(9) Katie Lank 11 Norton High School Norton, MA 78 (8+1)x9-sqrt(9) Beth Affanato 11 Norton High School Norton, MA 79 8x9+sqrt(9)!+1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 80 (8x9)+9-1 Nichole Howell 5 Johnson Elementary School Richmond, VA 81 (1x9)+(9x8) Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA 82 1+9+(9x8) Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA 83 (9+1)x8+sqrt(9) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 84 (8+1)x9+sqrt(9) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 85 (9+8)x((sqrt(9))!-1) Beth Affanato 11 Norton High School Norton, MA 86 (9+1)x8+(sqrt(9))! Cara Janczunski 11 Norton High School Norton, MA 87 (9x(8+1))+(sqrt(9))! Cheryl Morton 11 Norton High School Norton, MA 88 [(9x9)-1]+8 Stoy group 4 5 Stoy School Westmont NJ 89 9x9÷1+8 Jesse Gray 5 Johnson Elementary School Richmond, VA 90 9x9+8+1 Michael Lee 5 Johnson Elementary School Richmond, VA 91 ((sqrt(9))!)!÷8+1^9 Cara Janczunski 11 Norton High School Norton, MA 92 ((sqrt(9))!)!÷8+(sqrt(9)-1) Katie Lank 11 Norton High School Norton, MA 93 ((sqrt(9))!)!÷8+(sqrt(9)x1) Beth Affanato 11 Norton High School Norton, MA 94 ((sqrt(9))!)!÷8+(sqrt(9))+1 Cheryl Morton 11 Norton High School Norton, MA 95 (sqrt(9)+9)x8-1 Cheryl Morton 11 Norton High School Norton, MA 96 8x(sqrt(9)+1)xsqrt(9) Katie Lank 11 Norton High School Norton, MA 97 ((sqrt(9))!)!÷8+(sqrt(9))!+1 Casey Leavitt 11 Norton High School Norton, MA 98 9x(9+1)+8 NBCS group 7 7 Newark Boys Chorus School Newark,NJ 99 (8+sqrt(9))x9x1 Beth Affanato 11 Norton High School Norton, MA 100 (8+sqrt(9))x9+1 Beth Affanato 11 Norton High School Norton, MA
Please notify Judy Ann Brown of any errors.