All For 100

All For 100

Can you construct an expression for 100 which uses all the digits 1 to 9?

1

2

3

4

5

6

7

8

9

Shelf

 

That's correct. Can you find any other ways of doing it?

Topics: Starter | Arithmetic | Place Value | Problem Solving | Puzzles

  • Jake, Patana
  • Thursday, October 5, 2006
  • "I have found 1+2+3+4+5+6+7+8x9 = 100"
  • Lewis Crosby, Doncaster
  • Sunday, October 29, 2006
  • "I have found one too 198-73-26+5-4=100"
  • Sarah, Maidenhead
  • Tuesday, November 21, 2006
  • "Another solution for this is 56+49-2-3+8-7-1=100"
  • Katrina, Maidenhead
  • Tuesday, November 21, 2006
  • "I have got found another solution for this starter =
    6x7x2+8-3+1+9-4+5"
  • Holly, Whitby High, Ellesmere Port
  • Thursday, May 3, 2007
  • "Another Solution: (5x6)+(4x9)+(8x3)+7+2+1 = 100"
  • Reece & Ashlee, Ellesmere Port
  • Friday, May 4, 2007
  • "Two more solutions without brackets from Whitby High:

    123-4-5-6-7+8-9 = 100

    69+31+8+5-7-4-2 = 100"
  • James Wellington-Smith, Lea Moor High
  • Monday, May 7, 2007
  • "231-(9x8)-(6x5)-7-4"
  • Mr Heeley's Krew, Rawthorpe in da Hudd of field
  • Monday, October 1, 2007
  • "We found (1+9+2+8) x 5 + (3+7) - (4+6).

    We think that this is the best answer because simplicity is the key!

    Cushtie - please, please, please, please, please put us on the site.

    God bless you - Maths rocks"
  • Year 6, BIS Jakarta
  • Tuesday, October 2, 2007
  • "We found many solutions including
    9 * 4 * 2 + 8 + 7 + 3 + 5 + 6 - 1 = 100
    9 * 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100
    9 * 8 + 4 * 7 - 5 * 2 + 6 + 3 + 1 = 100"
  • Year 11- Mr Kelly's class, Cross and Passion College
  • Wednesday, October 3, 2007
  • "We found another solution for ALL FOR 100

    98+7-6+5-4+3-2-1=100"
  • Giovanni Fernandez, The British School of Quito, Ecuador
  • Wednesday, October 3, 2007
  • "2 x (7 x 8 x 9 - 456) + 3 + 1"
  • Tim Channer, The British School of Quito, Ecuador
  • Wednesday, October 3, 2007
  • "(9 x 8) + (7 x 6) - (5 x 4) + (3 x 2 x 1)"
  • Montae, Mrs. Shelburne's Period 3/6 class, Hayward Middle School, Springfield, Ohio
  • Thursday, October 4, 2007
  • "Here is Montae's solution...he found it in less than 5 minutes and creatively used exponents!

    5^2 x 4 - 9 + 6 + 3 - 7 + 8 - 1"
  • Ashleigh Reid, S2 Lochend Community High School
  • Friday, October 5, 2007
  • "I found this way of getting the answer:

    92 + 6 + 3 - 4 + 5 - 1 + 7 - 8"
  • Ciaran Donegan, Harrytown High School, Stockport, 8H
  • Friday, October 5, 2007
  • "I found (51+4+3) x 2 -9-8 + 7 -6"
  • Mrs Simpson, Torry Academy, Aberdeen
  • Friday, October 5, 2007
  • "2D1 Maths Class at Torry Acadmey found this way:

    89+7+6-5+(2*3)-4+1"
  • Andy Rowe, Knowles Hill School Devon
  • Friday, October 5, 2007
  • "Cameron Houdmont in Year 7 got this one

    (7 + 3) x 9 + 5 + 4 + 1 + 8 - 6 - 2"
  • Ms Winters, Dubai English Speaking College
  • Sunday, October 7, 2007
  • "Here are our answers from class 7DE...

    9x8+1+2+3+4+5+6+7

    6x3x5+12+4+(9-8)-7

    9x8+7+1+5x6-(4x3-2)"
  • Miss Train, Saints Peter and Paul
  • Sunday, October 7, 2007
  • "The first to get it in my class was Emma M in under 20 seconds - here's her solution:
    [(1+2+3+4) x 9] + 5 + 6 + 7 - 8 = 100"
  • Jodie, Lauren, Hayley, Harrytown High School Stockport
  • Monday, October 8, 2007
  • "123+45-67+8-9 Jodie Reilly 9T
    98-7-6+5+4+3+2+1 Lauren Hill 9W
    (1+2+3+4+5)x6-7+8+9 Hayley Ryder 9H"
  • Jack Houghton, Sydney, Australia
  • Wednesday, October 10, 2007
  • "I got 123+45-67+8-9"
  • Martin Vaughn, Central Sussex college haywards heath
  • Thursday, November 8, 2007
  • "8x9 +7 +1 +5 +6 +4 +3 +2 =100"
  • Jonathan, Holland Road
  • Friday, February 22, 2008
  • "the answer is
    12+34+59-6+8-7"
  • Miss Mian, Bishop Ramsey School, Ruislip
  • Thursday, March 13, 2008
  • "Daniela got the total by doing
    68 + 23 + 15 -4 +7 - 9

    and Amy got it by doing

    (9x8) + 1 + 2 + 3 + 4 + 5 + 6 + 7"
  • Josh Atkin, Dunbar Grammar
  • Wednesday, March 19, 2008
  • "The answer is
    (98-7) +1 -4 +6 -2 +3+5=100"
  •  

  • Mark Daniels, Wissahickon Middle School
  • Thursday, May 22, 2008
  • "Nicole from Mr. Daniels' Pre-Alg. Support class,WMS, Ambler,PA did this-
    4(5+7+8) + 1(2+3+6+9)

    Mr. Daniels offered this-
    2^5 + (8x9-4) + 13-(6+7)"
  • Mrs Simpson and class 4M4, Torry Academy, Aberdeen
  • Thursday, October 2, 2008
  • "Vincent found 963-852-7-4x1
    Emma found 6x9x2-8+4+1-3+5-7
    Shelby found 9x6+34+7+8-5+2x1
    Jasmine found 9x7+(6x8)-5-4-3-1+2"
  • Liam Hutchison, Lochend Community High School in Glasgow
  • Monday, October 6, 2008
  • "I calculated it this way

    (9x7) + 6 + 1 + (5 x 2) + (4 x 3) + 8"
  • Ellen Moore, KNGS, Birmingham,UK
  • Monday, October 6, 2008
  • "This works!
    (9+1)-(2+8)+(3+7)+(4+6)*5=100"
  • Miss Samantha Rhodes, Filsham Valley school, Hastings
  • Monday, October 6, 2008
  • "In 1 class, I had 5 different correct solutions.
    8x9+67+1-45+2+3 =100 (Charlotte Avery, year 8)
    5x19+34-28-7+6=100 (Sam Davies, year 8)
    3x4x6+2x9+(8-7+1)x5=100 (Sophie Fairall, year 8)
    8x9+1+2+3+4+5+6+7=100 (Charlotte Rudd, year 8)
    156-78+29-3-4=100 (James Bisson, year 8)"
  • Mr Jordan Fry, Laurence Jackson School, Guisbrough
  • Tuesday, October 14, 2008
  • "We got 5*9=45, 45+7=52, 52*2=104, 104-6=98, 98+4=102, 102-3=99, 99+1=100"
  • Emma, Lockerbie Academy
  • Tuesday, November 25, 2008
  • "78+24+9-6-5+3-2-1=100"
  • Soumya, Croydon
  • Wednesday, May 13, 2009
  • "1+8x9+2+7+6+5+3-4=100."
  • Form 7Y, Harrytown Catholic High School, Stockport
  • Tuesday, October 6, 2009
  • "Amy Booth found 9x8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100
    James Wilson (9x8) + 7 + 6 + 5 + (4 x 3) - (2 X 1) = 100."
  • Miss Marcham And 10f1, Prince Henry's High School, Evesham
  • Tuesday, October 6, 2009
  • "We got (6+4)x(8+9-7+5-3-2)x1 = 100."
  • Mrs J A Thompson, Mexborough School Specialist Science College
  • Wednesday, October 7, 2009
  • "Two different answers were found in 10 minutes. 7P SPECTRUM group
    The first was 1 + 2 + 3 + 4 + 5 +6 + 7 + (8x9) = 100 by Ashley Finney
    and (1+7+2) x 9 + 8 + (4x5)- (3x6) = 100 by Emma Rodgers."
  • Mitchel, Brocket
  • Thursday, October 8, 2009
  • "Another way of doing it is
    9-1=8, 8-2=6,7-3=4, 6-4=2, then
    8+6+4+2=20x5=100."
  • Y Ramsamy, Phoenix College, Reading, UK
  • Wednesday, October 14, 2009
  • "My pupils came up with the following solutions:
    (124-3-5-6-8-9)+7 = 100 Ryan Walsh
    (5x7x2x1)+3+4+6+8+9 = 100 Moin Khan
    Y Ramsamy
    Phoenix College, Reading, UK"
  • Jerry & Tom, Fukien School (HK)
  • Sunday, February 7, 2010
  • "(1+2x3x4)x5-6*7+8+9=100."
  • Thomas, Cabrach
  • Friday, September 3, 2010
  • "This wasn't easy but I found
    9x8+7+(6x4)-5+1+3-2=100."
  • Grade 12 Advanced Functions, Port Hope High School, Ontario, Canada
  • Wednesday, October 6, 2010
  • "Connor found 4x5x6-7-8-9-1+2+3
    Brandon found 24x5-9-8-7+6+1-3
    Brandon found 9x8+1+2+3+4+5+6+7."
  • Mrs Barnett & 8x1, Bredon Hill Middle School, Evesham
  • Wednesday, October 6, 2010
  • "Our simplest answer was (9x8)+7+6+5+4+3+2+1 = 100."
  • Greg Patko Yr8, Murray Park, Derby
  • Friday, October 8, 2010
  • "(9+8) x 7 - 6 x 5 + 4 x 3 + 1 - 2
    (1 + 9 + 2 + 8 + 3 + 7 - 6 - 4) x 5."
  • Mike Drewniak, Kewaskum Middle School
  • Friday, October 22, 2010
  • "Dinara found: 91+82-67-5-4+3."
  • Beacon Community College, Crowborough, 8XMa3
  • Thursday, July 7, 2011
  • "(6+4)x9+7+3+1+2+5-8=100."
  • David Clowes, St Peter's Academy
  • Wednesday, October 5, 2011
  • "I got 7x5x4-9x3-8-6+2-1."
  • Max, Hethersett Junior
  • Thursday, October 6, 2011
  • "12x5+39+6-8+7-4=100."
  • 9 (the Better Half) 1, Chellaston Academy, Derbyshire
  • Thursday, October 6, 2011
  • "Anneli and Molly: 9(6+3)+1+8+7+2+(5-4)
    May: 2(6x9-3-1+8-5-7+4)
    Rhys: 7x9+4x3+5+6x2+8x1
    David: 1(932-845)+6+7
    Eve: 5x6+87+1-9-4-3-2
    Ashley: 9x8+7+6+5+4x3-2x1."
  • 7ax1, Alexandra Park School, London
  • Friday, April 20, 2012
  • "Susie, Vinesha and Tommy : 8 x 9 + 7 + 1 + 6 + 5 + 4 + 2 + 3 = 100
    Semi (1 + 2 + 3 + 4 + 5) x 6 + (8 + 9) - 7 = 100
    Kira and Simon 341 - 265 + 9 + 7 + 8 = 100
    Ben 91 + 7 + 2 + 5 + 8 - 3 - 4 - 6 = 100
    Seb 123 - 45 - 67 + 89 = 100
    Lottie 8 x 9 x 2 - (4 x 5) - (6 x 3) - 7 + 1 = 100
    Peter (1 + 2 + 3) x 6 - 7 - 5 - 8 + 9 x 4 = 100."
  • Australia Class, Cottam, Preston, England
  • Thursday, July 12, 2012
  • "Our class found 2 ways to solve this puzzle:
    8x9=72+(5x4)=92+(7+1)=100-6=94+2x3=100
    The next idea is:2+8= 10X9=90+5=95+6=101+4=105+3=108-1=107-7=100."
  •  

  • RM, UK
  • Wednesday, September 12, 2012
  • "I have found: 1 x 7 x 9 + 2 x 6 + 4 x 5 + 8 + 3 = 100."
  • Abi T, St Peter's Y6 Maths Group
  • Monday, October 1, 2012
  • "(9x8)x1 +6 +7 + (5x4)- (3+2)."
  • Miss Brook, Crick Primary School
  • Tuesday, October 2, 2012
  • "William - Year 6 - 9x8=72 + 5x6 - 7 - 2 - + 3 + 4 x 1
    Ethan - Year 6 - 7x9 x 2 - 8 - 6 - 5 - 3 - 4 x 1."
  • Taeh, Croydon
  • Friday, October 19, 2012
  • "I found out that you can do 8x9 which equals 72 and then you add 7+6+5+4+3+2+1=28 then 28 and 72 equals 100."
  • Sophie Tune, Kingswinford England
  • Tuesday, October 30, 2012
  • "I got 1+2+3+4+5x7(105)-6+9-8."
  • Matthew Zhao, 4AD, Craigslea State School
  • Monday, October 14, 2013
  • "Matthew Zhao here, coming with with a personal answer in two minutes!
    47*2+1+3+6+9-8-5=100.
    (P.S. I'm in Grade Four)."
  • Mr Macready, Jersey
  • Friday, February 14, 2014
  • "Sarah here in Jersey Year 8.1 came up with (93+7)+(8x6)-45-2-1
    Some of the others came up with answers like 99.2, which aren't 100 last time I checked!"

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Answers

See comments above for many different solutions.

Here are some solutions to a similar puzzle from a book published in 1908:

Answers


Laptops In Lessons

Teacher, do your students have access to computers?
Do they have Laptops in Lessons or iPads?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here is the URL for a concise version of this page without comments or answers.

Transum.org/go/?Start=October6

Here is the link which will take them to a student version of this activity with different levels for which they can earn Transum Trophies!

Transum.org/go/?to=Centex

 

 

Extension Activity

Use the digits zero to nine to make the first ten digits (one at a time!)




 

Extension Answers

Here are the solutions to the extension challenge as published in 'A Scrap-Book of Elementary Mathematics' in 1908:

Extension Answers

Apple

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