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All the King's Digits

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View All the King's Digits Sister Site at The World of Trotter Math.

This solutions page presents a special challenge that we'll call "The Tail of the Dog". It simply means the expression has two parts: a body composed of eight non-zero digits, and a tail composed of the zero (0) and the remaining non-zero digit. See solutions #52-#60.

The tail can be connected to the body in one of three ways:

  • "body = 100" + 0 * d [or 0^d] (where d is that remaining ninth digit), or
  • "body = 100" * d^0
  • "body = 99" + d^0

A good example of the first expression structure was done by Eric Kissinger, #3 (on the first page of solutions). A good example of the second expression structure was done by Ellen Li, #36. The third expression structure was done by Jerod Dai, #32. Please take a look at them.

This means that in the future a solution such as this:

(49 + 51) + (235678)(0)

possibly won't be posted for lack of creativity and general interest. Ok?

The submissions below arrived from February 18 till March 6, 2001.

STUDENT SOLUTIONS

# Solution Name (Grade) School
41 (9*8) + (4*7) + 0(1+2+3+5+6) Jeffrey Wang (8) Taipei American School
42 (42 + 8)(6^1 3)/579^0 Mindy Hiesmantjaja (8) Taipei American School
43 25*4 + 0(1-3-6-7-8-9) Hritrik Brian Roshan (10) Middlefield Coligiate Institute
44 96+4+(1+2+3+5+7+8)(0) Ryan Tackaberry (8) Taipei American School
45 sqrt[E4[(53 * 19 - 7 )268^0]] Yejay Ying (8) Taipei American School
46 (7!/E6)^2/[((5+3)^(cbrt(8)/
(sqrt(4-1))^0))*9]
Giacomo Biccardo (12) Liceo Scientifico Righi
47 E8+E9+7+6+5+1+ 0*(2+3+4) Dan Chen (8) Taipei American School
48 5^2 + 9 x 8 + (3 - 1) + (7 + 6 + 4)^0 Tomomi Tokue (8) Taipei American School
49 908 - 765 - 43 * (2 - 1) Nina Huang (8) Taipei American School
50 (9 + 1)^2 + 3 + 7 - 6 - 4 + 8(5 * 0) Casey Sapp (10) Winter Springs High School
51 (9*8*2) - (6*5) - (7 + 4 + 3) + (1*0) Jonathan Clark (11) Winter Springs High School
52 (264/8)+(9*5)+(7*3)+ 1^0 Anna Liao (8) Boston Latin
School
53 98 + (7 - 6) - (5 - 4) + (3 - 1) + 2*0 Joshua Zucker Castilleja
School
54 2(4*5) + (6*7) + (9+8+1) + 3(0) Christine Creanza (10) Winter Springs High School
55 (((((5*7) + (9+6)/(3-1)) * 8)/2) * 4^0 Jayashree Gandhi (5) Somerville Charter School
56 [(9 * 8)/3 * 4 + 7 + 2 - 6 + 1] + [5*0] Tommy Lubrano (11) Winter Springs High School
57 (4^2)/8 + (1 * 7 * 9) + 35 + 0^6 Lindsay Braun (10) Winter Springs High School
58 9 * 8 + 13 + 4 * 5 - 6 + 2 - 7^0 Brandon Grayson (11) Winter Springs High School
59 76 + (3 * 4) + 9^1 + (5 - 2)- (8 * 0) Kyle Ginzl (11) Winter Springs High School
60 (1^8) + (3!) + (4*5*6) - (27) + (9*0) Tiffany Tibbets (10) Winter Springs High School

Solutions #1 to #20
Solutions #21 to #40
Solutions #61 to #80
Solutions #81 to #100
Solutions #101 to #120
Solutions #121 to #140
Solutions #141 to #160

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