#### 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

## STUDENT SOLUTIONS

 Solution Name Grade School 1 (sqrt(9)+8)-(9+1) Stoy group 2 5 Stoy School Westmont NJ (9!÷8!) - 9 + 1 Rachel Huitt 11 Calamus-Wheatland Jr. Sr. High School Wheatland IA 8-(1+sqrt(9)+sqrt(9)) Eric Todd 8 Nichols Middle School Buffalo, NY 2 sqrt(9)+8-(9x1) Stoy group 2 5 Stoy School Westmont NJ (9+9)÷(8+1) Eric Todd 8 Nichols Middle School Buffalo, NY (9+8+1)÷9 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School 3 (sqrt(9)+9)-(8+1) Stoy group 2 5 Stoy School Westmont NJ 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 (sqrt(9)+1)÷(9-8) Eric Todd 8 Nichols Middle School Buffalo, NY sqrt[(9÷9 +1)x8] William Simpson 6 Newark Boys Chorus School, Newark, NJ 5 (sqrt(9)+9)-(8-1) Stoy group 2 5 Stoy School Westmont NJ (sqrt(9))+(9+1-8) Eric Todd 8 Nichols Middle School Buffalo, NY 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 8-(9÷9+1) NBCS group 7 7 Newark Boys Chorus School Newark,NJ sqrt(9) + sqrt(9)x1^8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 7 (8-1)+(9-9) Stoy group 5 5 Stoy School Westmont NJ (sqrt(9-1+8)+(sqrt(9)) Eric Todd 8 Nichols Middle School Buffalo, NY 9+8-1-9 Michael Lee 5 Johnson Elementary School Richmond, VA 9-9+8-1 Jesse Gray 5 Johnson Elementary School Richmond, VA 9x8÷9-1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School 8 (1x8)+(9-9) Stoy group 5 5 Stoy School Westmont NJ (9-8)(9-1) Eric Todd 8 Nichols Middle School Buffalo, NY 9+8x1-9 Kristen Marshall 5 Johnson Elementary School Richmond, VA 9x1+8-9 Michael Lee 5 Johnson Elementary School Richmond, VA 9-9+1x8 Zohaib Damani 5 Johnson Elementary School Richmond, VA (9÷1)÷(9÷8) Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (9÷9)+8-1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (9÷9)x8x1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (9÷9)x8÷1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School 9 (8+1)+(9-9) Stoy group 5 5 Stoy School Westmont NJ 9+9-1-8 Rachel Huitt 11 Calamus-Wheatland Jr. Sr. High School Wheatland IA (9+9)-(8+1) Eric Todd 8 Nichols Middle School Buffalo, NY 9+1-9+8 Michael Lee 5 Johnson Elementary School Richmond, VA 9-9+1+8 Zohaib Damani 5 Johnson Elementary School Richmond, VA (1÷9)x9+8 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (-9)-(-9)-(-8)+1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (9÷9)x8+1 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School (9÷9)x8-(-1) Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School 10 (9÷9)+(8+1) Stoy group 5 5 Stoy School Westmont NJ (9+9-8)÷1 Eric Todd 8 Nichols Middle School Buffalo, NY 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 (9+9)-(8-1) Eric Todd 8 Nichols Middle School Buffalo, NY 12 sqrt(9) + 9x1^8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 13 sqrt(9)+sqrt(9)+8-1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ sqrt(9+8-1)+9 Katie Hayen 9 Calamus-Wheatland Jr. Sr. High School Wheatland, IA 14 1x(sqrt(9)+sqrt(9)+8) NBCS group 8 8 Newark Boys Chorus School Newark,NJ 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 9+8+1-sqrt(9) MOMS group 8 8 Mt. Olive Middle School Budd Lake, 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 sqrt(9)x9-8+1 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 9÷sqrt(9)x8+1 NBCS group 8 8 Newark Boys Chorus School Newark,NJ 8-1+9+9 Brittney Anderson 5 Johnson Elementary School Richmond, VA 26 (9+8)+(9÷1) Stoy group 8 5 Stoy School Westmont NJ (1x9)+9+8 Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA 9+9x1+8 Zohaib Damani 5 Johnson Elementary School Richmond, VA 9xsqrt(1)+8+9 Michael Lee 5 Johnson Elementary School Richmond, VA 27 (1+8)+(9+9) Stoy group 5 5 Stoy School Westmont NJ 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 [(8+1)/9]+9!!!!!! Stoy group 8 5 Stoy School Westmont NJ 29 (9!/8!)+[(9+1)!!!!!!!! Stoy group 8 5 Stoy School Westmont NJ 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))!)!)÷sqrt(9))÷8+1 Cara Janczunski 11 Norton High School Norton, MA ((sqrt(9))!-1)x8-9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ (sqrt(9)x8)+(sqrt 9)! +1 11 Norton High School Norton, MA 9!!!!!! + 8-sqrt(9) -1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ sqrt[(9!!+8) + (9-1)] Vinnie Westphal 6 Mount Olive Middle School Budd Lake, NJ 32 (9-1)xsqrt(9)+8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 33 (8xsqrt(9))+9÷1 Katie Lank 11 Norton High School Norton, MA 8xsqrt(9)+9x1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 9!!!!!! + sqrt(9)!x1^8 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 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 (9!÷8!)(sqrt(9)+1) NBCS group 8 8 Newark Boys Chorus School Newark,NJ 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 [sqrt(9)]!x[sqrt(9)!]+1 Vinnie Westphal 6 Mount Olive Middle School Budd Lake, NJ 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 8!!!!+ 9x1^9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ 8x[sqrt(9)+1]+9 Vinnie Westphal 6 Mount Olive Middle School Budd Lake, NJ 42 (sqrt(9))!x8-(sqrt(9))!÷1) Casey Leavitt 11 Norton High School Norton, MA 8!!!! +9+1^9 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ [sqrt(9)]!x(8-1^9) Vinnie Westphal 6 Mount Olive Middle School Budd Lake, NJ 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 (9!!!!+9)-(8x1) Stoy group 3 5 Stoy School Westmont NJ 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 [(9!!!!!!+8!!!!)-(9+1)=49 Stoy group 3 5 Stoy School Westmont NJ 8x(sqrt(9)+sqrt(9))+1 Katie Lank 11 Norton High School Norton, MA 50 sqrt(9)!x8+sqrt(9) -1 MOMS group 8 8 Mt. Olive Middle School Budd Lake, NJ (8-sqrt(9))x( 9+ 1) Katie Lank 11 Norton High School Norton, MA 51 sqrt(9)!x8+sqrt(9)x1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ sqrt(9)x(8+(9x1)) Cara Janczunski 11 Norton High School Norton, MA sqrt(9)!x8+(sqrt(9)x1) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 52 sqrt(9)!x8+sqrt(9)+1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9+8)xsqrt(9)+1 Katie Lank 11 Norton High School Norton, MA sqrt(9)!x8+(sqrt(9)+1) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 53 9x((sqrt(9))!-1)+8 Beth Affanato 11 Norton High School Norton, MA 9x(sqrt9)!-1^8 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 9xsqrt(9)!-1^8 Dan Schronda 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 (sqrt(9)!+1)x8+sqrt(9) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 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 (9x8)-(9+1) Stoy group 7 5 Stoy School Westmont NJ (8x9)-9-1 Brittney Anderson 5 Johnson Elementary School Richmond, VA 63 (9x8)-(9x1) Stoy group 7 5 Stoy School Westmont NJ 9x8-9÷1 Julia D'Rozario 5 Johnson Elementary School Richmond, VA 8÷1x9-9 Michael Lee 5 Johnson Elementary School Richmond, VA 9x8÷1-9 Michael Lee 5 Johnson Elementary School Richmond, VA 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 8x9-(sqrt(9)!)x1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 9x(8-1)+sqrt(9) Casey Leavitt 11 Norton High School Norton, MA (8+sqrt(9))xsqrt(9)!x1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 67 8x9-(sqrt(9)!-1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 8x(9-1)+sqrt(9) Beth Affanato 11 Norton High School Norton, MA (8+sqrt(9))xsqrt(9)!+1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 68 8x9-(sqrt(9)+1) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9x8)-sqrt(9)-1 Beth Affanato 11 Norton High School Norton, MA 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 8x9-sqrt(9)+1 Cara Janczunski 11 Norton High School Norton, MA 71 8x(9+1)-9 NBCS group 6 6 Newark Boys Chorus School Newark,NJ (1+9)x8-9 Nichole Howell 5 Johnson Elementary School Richmond, VA 72 [(9x9)-8]-1 Stoy group 6 5 Stoy School Westmont NJ 9x9-1-8 Megan Gersch 5 Johnson Elementary School Richmond, VA 73 [(9x1)x9]-8 Stoy group 6 5 Stoy School Westmont NJ 9x9x1-8 Kristen Marshall 5 Johnson Elementary School Richmond, VA 9÷1x9-8 Megan Gersch 5 Johnson Elementary School Richmond, VA 74 [(9x9)-8]+1 Stoy group 6 5 Stoy School Westmont NJ 9x9+1-8 Kristen Marshall 5 Johnson Elementary School Richmond, VA 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 sqrt(9)+8x9+1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 9x8+sqrt(9)+1 Katie Lank 11 Norton High School Norton, MA 77 8x9+sqrt(9)!-1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9+1)x8-sqrt(9) Katie Lank 11 Norton High School Norton, MA 78 8x9+sqrt(9)!x1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (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 9x8+9-1 NBCS group 6 6 Newark Boys Chorus School Newark,NJ 9x(9-1)+8 NBCS group 7 7 Newark Boys Chorus School Newark,NJ (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 (8x9)+1+9 Kristen Marshall 5 Johnson Elementary School Richmond, VA 82 1+9+(9x8) Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA (9+1)x9-8 Kristen Marshall 5 Johnson Elementary School Richmond, VA 8x9+1+9 Megan Gersch 5 Johnson Elementary School Richmond, VA 83 (9+1)x(8)+sqrt(9) Cheryl Morton 11 Norton High School Norton, MA 8!!!+sqrt(9)x1^9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9+1)x8+sqrt(9) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 84 8!!!+sqrt(9)+1^9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 9x9+sqrt(8+1) Katie Lank 11 Norton High School Norton, MA (8+1)x9+sqrt(9) Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 85 8!!!+sqrt(9)!-1^9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9+8)x((sqrt(9))!-1) Beth Affanato 11 Norton High School Norton, MA (8+sqrt(9)!)xsqrt(9)!+1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 86 (9+1)x8+(sqrt(9))! Cara Janczunski 11 Norton High School Norton, MA 8!!!+sqrt(9)!x1^9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (9+1)x8+sqrt(9)! Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 87 (9x(8+1))+(sqrt(9))! Cheryl Morton 11 Norton High School Norton, MA 8!!!+sqrt(9)!+1^9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (8+1)x9+sqrt(9)! Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 88 [(9x9)-1]+8 Stoy group 4 5 Stoy School Westmont NJ 9x9+8-1 Nikki Howell 5 Johnson Elementary School Richmond, VA 89 [(9x9)+8]÷ 1 Stoy group 4 5 Stoy School Westmont NJ 9x9÷1+8 Jesse Gray 5 Johnson Elementary School Richmond, VA 90 (1+8)+(9x9) Stoy group 4 5 Stoy School Westmont NJ 1+(9x9)+8 Liz McDonnell 10 Calamus-Wheatland Jr. Sr. High School Wheatland IA 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 8!!!+sqrt(9)+9-1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (sqrt(9)!)!÷8+1^9 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 92 8!!!+sqrt(9)+9^1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ ((sqrt(9))!)!÷8+(sqrt(9)-1) Katie Lank 11 Norton High School Norton, MA (sqrt(9)!)!÷8+sqrt(9)-1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 93 ((sqrt(9))!)!÷8+(sqrt(9)x1) Beth Affanato 11 Norton High School Norton, MA 8!!!+sqrt(9)+9+1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (sqrt(9)!)!÷8+sqrt(9)x1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 94 ((sqrt(9))!)!÷8+(sqrt(9))+1 Cheryl Morton 11 Norton High School Norton, MA 8!!!+9!!!!!!!-sqrt(9)-1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (sqrt(9)!)!÷8+sqrt(9)+1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 95 (sqrt(9)+9)x8-1 Cheryl Morton 11 Norton High School Norton, MA 8!!!+9!!!!!!!-sqrt(9)x1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 96 8!!!+(9+1)+sqrt(9)! MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 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 8!!!+9+9-1 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ 9^2+8-1+9 Mellissa Mccole 9 Delaware Valley High School Milford PA 98 9x(9+1)+8 NBCS group 7 7 Newark Boys Chorus School Newark,NJ (1+9)x9+8 Nichole Howell 5 Johnson Elementary School Richmond, VA 99 (8+sqrt(9))x9x1 Beth Affanato 11 Norton High School Norton, MA 8!!!+(9+1)+9 MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (8+sqrt(9))x9x1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ 100 (8+sqrt(9))x9+1 Beth Affanato 11 Norton High School Norton, MA (9!!!!!!+1)+(9x8) MOMS group 8 8 Mount Olive Middle School Budd Lake, NJ (8+sqrt(9))x9+1 Dan Schronda 8 Mount Olive Middle School Budd Lake, NJ
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Web page created by Judy Ann Brown on Saturday, January 10, 1998.