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

1

2

3

4

5

6

7

8

9

###### That's correct. Can you find any other ways of doing it?
• You can put numbers together to make larger numbers, for example. 53, 127 etc.
• Don't forget the order of operations, BIDMAS, when evaluating your expressions.
• Surprisingly there's a solution in which all of the digits remain in numerical order.

## A Mathematics Lesson Starter Of The Day

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

God bless you - Maths rocks
• Year 6, BIS Jakarta
•
• 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
•
• 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
•
• 2 x (7 x 8 x 9 - 456) + 3 + 1
• Tim Channer, The British School of Quito, Ecuador
•
• (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
•
• 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
•
• I found this way of getting the answer:

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

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

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

(9x7) + 6 + 1 + (5 x 2) + (4 x 3) + 8
• Ellen Moore, KNGS, Birmingham,UK
•
• This works!
(9+1)-(2+8)+(3+7)+(4+6)*5=100
• Miss Samantha Rhodes, Filsham Valley school, Hastings
•
• 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
•
• We got 5*9=45, 45+7=52, 52*2=104, 104-6=98, 98+4=102, 102-3=99, 99+1=100
•
• 78+24+9-6-5+3-2-1=100
• Soumya, Croydon
•
• 1+8x9+2+7+6+5+3-4=100.
• Form 7Y, Harrytown Catholic High School, Stockport
•
• 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
•
• We got (6+4)x(8+9-7+5-3-2)x1 = 100.
• Mrs J A Thompson, Mexborough School Specialist Science College
•
• 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
•
• 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
•
• 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
• Jerry & Tom, Fukien School (HK)
•
• (1+2x3x4)x5-6*7+8+9=100.
• Thomas, Cabrach
•
• This wasn't easy but I found
9x8+7+(6x4)-5+1+3-2=100.
•
• 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
•
• Our simplest answer was (9x8)+7+6+5+4+3+2+1 = 100.
• Greg Patko Yr8, Murray Park, Derby
•
• (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
•
• Dinara found: 91+82-67-5-4+3.
• Beacon Community College, Crowborough, 8XMa3
•
• (6+4)x9+7+3+1+2+5-8=100.
• David Clowes, St Peter's Academy
•
• I got 7x5x4-9x3-8-6+2-1.
• Max, Hethersett Junior
•
• 12x5+39+6-8+7-4=100.
• 9 (the Better Half) 1, Chellaston Academy, Derbyshire
•
• 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
•
• 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
•
• 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
•
• 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
•
• 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
•
• I got 1+2+3+4+5x7(105)-6+9-8.
• Matthew Zhao, 4AD, Craigslea State School
•
• Matthew Zhao here, coming with with a personal answer in two minutes!
47*2+1+3+6+9-8-5=100.
•
• 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!
•
• I found 9x8+7+6+5+4+3+2+1 which makes 100.
• Mr. Van, Sweden
•
• We did it!
• Shaa, India
•
• 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
•
• 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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## Extension Activity

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