Two Dice
Joe Densley from Clutton Primary had this send for hom with the comments;
Joe worked systematically to find all the possible combinations for throwing 2 dice. He identified the lowest possible score of 2 and the highest score of 12. At first he thought that 4 was the lowest score and was then able to correct himself.
Robert from St.Michael's Primary West Midlands sent in this very thorough solution;
There are eleven possible solutions to 'Two Dice'.
Let's say Dice One is 'A' and Dice Two is 'B'.
They are as follows :
$2$ (A=$1$ and B=$1$)
$3$ (A=$1$ and B=$2$; A=$2$ and B=$1$)
$4$ (A=$1$ and B=$3$; A=$2$ and B=$2$; A=$3$ and B=$1$)
$5$ (A=$1$ and B=$4$; A=$2$ and B=$3$; A=$3$ and B=$2$; A=$4$ and B=$1$)
$6$ (A=$1$ and B=$5$; A=$2$ and B=$4$; A=$3$ and B=$3$; A=$4$ and B=$2$; A=$5$ and B=$1$)
$7$ (A=$1$ and B=$6$; A=$2$ and B=$5$; A=$3$ and B=$4$; A=$4$ and B=$3$; A=$5$ and B=$2$; A=$6$ and B=$1$)
$8$ (A=$2$ and B=$6$; A=$3$ and B=$5$; A=$4$ and B=$4$; A=$5$ and B=$3$; A=$6$ and B=$2$)
$9$ (A=$3$ and B=$6$; A=$4$ and B=$5$; A=$5$ and B=$4$; A=$6$ and B=$3$)
$10$ (A=$4$ and B=$6$; A=$5$ and B=$5$; A=$6$ and B=$4$)
$11$ (A=$5$ and B=$6$; A=$6$ and B=$5$)
$12$ (A=$6$ and B=$6$)
Two $1-6$ dice will not add up to any other number. This solution shows the
amount of numbers possible to make. However there are 36 possible
combinations of numbers to create the 11 possible answers.