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


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.
  • , Myrtleford
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  • I have managed to find a way of getting so many firstly you two numbers to be a ninety type number aka 9 and 6 then you add to make 100 so in this case 4 then you the rest of the numbers to add and subtract what you have added on so now it's 96+4+8-7-1+5-3-2 making countless ways of doing it!!

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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

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

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How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

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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.

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Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

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

Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

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Another Craig Barton Book

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more... #ad

Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more... #ad

A Compendium Of 	Mathematical Methods

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... #ad

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

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Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more... #ad

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

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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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