All For 100

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

1

2

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5

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7

8

9

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

A Mathematics Lesson Starter Of The Day


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

  • Jake, Patana
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  • I have found 1+2+3+4+5+6+7+8x9 = 100
  • Lewis Crosby, Doncaster
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  • I have found one too 198-73-26+5-4=100
  • Sarah, Maidenhead
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  • Another solution for this is 56+49-2-3+8-7-1=100
  • Katrina, Maidenhead
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  • I have got found another solution for this starter =
    6x7x2+8-3+1+9-4+5
  • Holly, Whitby High, Ellesmere Port
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  • Another Solution: (5x6)+(4x9)+(8x3)+7+2+1 = 100
  • Reece & Ashlee, Ellesmere Port
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  • 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
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  • 231-(9x8)-(6x5)-7-4
  • Mr Heeley's Krew, Rawthorpe in da Hudd of field
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  • 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
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  • 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
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  • 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
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  • 2 x (7 x 8 x 9 - 456) + 3 + 1
  • Tim Channer, The British School of Quito, Ecuador
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  • (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
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  • 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
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  • I found this way of getting the answer:

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

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

    (7 + 3) x 9 + 5 + 4 + 1 + 8 - 6 - 2
  • Ms Winters, Dubai English Speaking College
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  • 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
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  • 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
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  • 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
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  • I got 123+45-67+8-9
  • Martin Vaughn, Central Sussex college haywards heath
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  • 8x9 +7 +1 +5 +6 +4 +3 +2 =100
  • Jonathan, Holland Road
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  • the answer is
    12+34+59-6+8-7
  • Miss Mian, Bishop Ramsey School, Ruislip
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  • 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
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  • The answer is
    (98-7) +1 -4 +6 -2 +3+5=100
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  • Mark Daniels, Wissahickon Middle School
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  • 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
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  • 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
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  • I calculated it this way

    (9x7) + 6 + 1 + (5 x 2) + (4 x 3) + 8
  • Ellen Moore, KNGS, Birmingham,UK
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  • This works!
    (9+1)-(2+8)+(3+7)+(4+6)*5=100
  • Miss Samantha Rhodes, Filsham Valley school, Hastings
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  • 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
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  • 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
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  • 78+24+9-6-5+3-2-1=100
  • Soumya, Croydon
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  • 1+8x9+2+7+6+5+3-4=100.
  • Form 7Y, Harrytown Catholic High School, Stockport
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  • 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
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  • We got (6+4)x(8+9-7+5-3-2)x1 = 100.
  • Mrs J A Thompson, Mexborough School Specialist Science College
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  • 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
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  • 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
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  • 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)
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  • (1+2x3x4)x5-6*7+8+9=100.
  • Thomas, Cabrach
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  • 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
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  • 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
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  • Our simplest answer was (9x8)+7+6+5+4+3+2+1 = 100.
  • Greg Patko Yr8, Murray Park, Derby
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  • (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
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  • Dinara found: 91+82-67-5-4+3.
  • Beacon Community College, Crowborough, 8XMa3
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  • (6+4)x9+7+3+1+2+5-8=100.
  • David Clowes, St Peter's Academy
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  • I got 7x5x4-9x3-8-6+2-1.
  • Max, Hethersett Junior
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  • 12x5+39+6-8+7-4=100.
  • 9 (the Better Half) 1, Chellaston Academy, Derbyshire
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  • 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
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  • 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
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  • 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.
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  • RM, UK
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  • 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
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  • (9x8)x1 +6 +7 + (5x4)- (3+2).
  • Miss Brook, Crick Primary School
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  • 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
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  • 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
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  • I got 1+2+3+4+5x7(105)-6+9-8.
  • Matthew Zhao, 4AD, Craigslea State School
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  • 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
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  • 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!
  • Gurdev Rayet, Holyheadschool
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  • I found 9x8+7+6+5+4+3+2+1 which makes 100.
  • Mr. Van, Sweden
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  • We did it!
  • Shaa, India
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  • It's really cool, do you want to see more?

    _ _ +_ _+_ _ = _ _+ _=100

    Fill in the blanks with the numbers from 1 to 9 without repeating.

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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



Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Equate board game

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Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

iPad Air

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You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Aristotle's Number Puzzle

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This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

Click the images above to see all the details of these gift ideas and to buy them online.


Laptops In Lessons

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

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

Laptops In Lessons

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

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

Student Activity

 

 

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

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