Copyright © University of Cambridge. All rights reserved.

'Highest and Lowest' printed from http://nrich.maths.org/

Show menu


We had nearly $100$ solutions submitted to us with acceptable ideas for the highest and lowest. Five schools sent in many submissions and quite a few students went on to explore what they could do with $1, 2, 3, 4, 5$ and $6$.

Banstead Junior School pupils George, Marcus, Ellanah, Ellie, Grace and Lauren sent in individual solutions that showed $360$ as the highest number and $0$ as the lowest. They went on to show that with more numbers they could get as high as $720$.

Norwayne Elementary School in the USA pupils, Kyler, Tim, Wesley and Grace also sent in individual solutions and extended the lowest down to $0.025$.  When using the $6$, numbers got as low as $1-65432 = -65431$.


Hamilton Academy pupils Saihaan, Sean, Theo and Huda individually took the lowest number down to $-36$.

Bowes Primary School pupils Yasara, Chloe, Shiv, Rhea, Lotte, and Aan individually took  it
down to $-19$ using the six numbers.

Heage Primary School pupils Fraser, Brogan, Miles and Phoebe individually took using six numbers up to $1080$.

Matthew from  Beechwood Park School
 sent in this which is typical of many of the solutions sent in;


Highest: $(2$x$3)$x$(4$x$5)$x$6=720$   Lowest:$1-2-3-4-5-6=-21$

Annabelle from Toongabbie Christian School
 in Australia
 sent in this for the first part of the problem which represents many students' workings:

$3$x$4$x$5$x$6$ highest             $3-4-5-6$ lowest

Tritham from St.Christopher's 
School Penang, Malyasia sent in the following for the smallest answer:

The smallest answer is $6-5-(4-3)=0$

Finally at the end of the month we had this submission from Year $5$ at St. Ambrose School:

Highest:  $63$x$54= 3402$  and Lowest: $3-654= -651$.

Well you certainly worked hard on this activity. Well done all of you. We hope to hear from you again soon.