Solution to SGC Maths Quest 3: A bit of a dicey problem

St George’s College, Weybridge invited children from Years 5 and 6 at all local schools to take part in the third instalment of the SGC Maths Quest challenge.

Each Half Term, St George’s College will provide a Maths problem for children from Years 5 and 6 to solve. All correct entries will be displayed on the St George’s Weybridge website at www.stgeorgesweybridge.com

Solution to SGC Maths Quest 3: A bit of a dicey problem

Thank you to everyone who submitted answers. Well done to all of you who provided a solution, there were six excellent solutions sent in, keep up the good work!

Below is a list of the winners and how each of them came up with the solution and solved the puzzle.

Magdalena West, Year 5, St George’s Junior School, Weybridge.

Magdalena's Solution - The possible results with 6 sided dice are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

There are 36 possible combinations in total. You have the highest chance of rolling 7, as there are six different combinations:

1 & 6, 2 & 5, 3 & 4, 6 & 1, 5 & 2, 4 & 3.

There are 100 possible results with 10 sided dice - 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 100 combinations is the total.

Akhil Kapoor, Year 5 Hall Grove School, Bagshot.

Akhil's solution - My answer to the maths quest is 7 for the six sided dice. This is because you get the most combinations with the number between 1-6 to make 7. 

For the 10 sided dice the answer is 11. Again this is because you get the most combinations of numbers to make 11 with numbers between 1-10.

I worked it out by putting the answers in a table and found that the answer ran diagonally through the middle.

Katie Linn, Year 6, St. George's Junior School, Weybridge.

Katie's solution - When you have two ordinary dice, results could be: 2,3,4,5,6,7,8,9,10,11 or 12. You have more chance of getting 7 because you can get this answer with a combination that includes each number: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1.

If you have a 10 sided dice you could get every value from 2 to 20. You have most chance of getting 11 because there is a combination possible with every value on the dice

Monty Nendick, Year 5, Claremont Fan Court School.

Monty's solution - If you throw 2 six sided dice you can get any answer from 2 to 12. The most common answer will be 7. This is because there are 6 ways that you can throw a seven (more than any other answer):

1 & 6, 6 & 1, 2 & 5, 5 & 2, 3 & 4, 4 & 3.

If you throw two 10 sided dice you can get any answer from 2 to 20. The most common answer is 11 which you can get by throwing:

1 & 10, 10 & 1, 2 & 9, 9 & 2, 3 & 8, 8 & 3, 4 & 7, 7 & 4, 5 & 6, 6 & 5, making 10 ways.

Charlie Hampele, Year 5, Bishopsgate School.

Charlie's solution - When you roll together two ordinary six faced dice you could get results of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

You have more of a chance of getting 7 because there are 6 sums to add up to 7 which are 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3.

 If you use a dice with 10 numbers on you could get answers of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20.

You have more of a chance of getting 11 because even though 11 and 12 are the 2 middle numbers and have 10 number bonds, you can’t do 11 + 1 because you don’t have an 11 on the dice. With 11 you have 10 sums you can use which are 1 + 10, 10 + 1, 9 + 2, 2 + 9, 8 + 3, 3 + 8, 7 + 4, 4 + 7, 6 + 5 and 5 + 6. 

And our final winner was Blake Cooke, Year 5, Bishopsgate School.

Please watch out for SGC Maths Quest 4, which will be published on Tuesday 18 April 2017.

Here is the original problem:

Download the full Maths Quest here.

20 February 2017

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