Add 3 dice
Problem
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice.
Can you find all the ways to do this?
Printable NRICH Roadshow resource.
Student Solutions
Daniel (Age 10, Anglo-Chinese School, Singapore) pointed out a fact about the way the numbers are placed on dice. This is particularly important to remember if you don't have any real ones to work with.
I have put everyone's solutions together into a table so that it will be easy to check whether you have found a new one or not.
Kieran (Age 10) & Carl (Age 9, Moorgate C.P. School) - 1 solution
Christina (Age 11, Marlborough Primary School) - 1 solution
Caroline & Sarah (Year 7, The Mount School, York) - 4 solutions
Leah (Age 10) & Sophie Simpson (Age 11, Moorgate C.P. School) - 11 solutions
Edward (Age 10, Tattingstone School) - 14 solutions - Well done!!
| TOTAL | TOP NUMBERS | FRONT NUMBERS |
|---|---|---|
| 5 | 2 2 1 | 1 1 3 |
| 6 | 1 4 1 2 2 2 |
3 2 1 4 1 1 |
| 7 | 1 4 2 2 3 2 |
2 1 4 1 5 1 |
| 8 | 2 5 1 | 1 4 3 |
| 9 | 5 2 2 3 3 3 2 1 6 |
1 4 4 1 2 6 1 5 3 |
| 10 | 6 3 1 3 6 1 5 4 1 |
4 2 4 2 3 5 4 1 5 |
| 11 | 5 4 2 | 1 6 4 |
| 12 | 4 4 4 5 6 1 5 2 5 |
1 6 5 4 5 3 4 4 4 |
| 13 | 5 3 5 6 2 5 |
1 6 6 3 4 6 |
| 14 | 5 4 5 6 2 6 |
3 5 6 3 6 5 |
| 15 | 6 6 3 5 6 4 6 3 6 |
4 6 5 4 5 6 5 5 5 |
| 16 | 5 6 5 | 6 6 4 |
During 2015 we had another solution sent in showing other numbers on the dice that would work, here it is.
Yr 3/4 children from St Peter Julian Eymard in Australia sent in these
| Total | Top | Side |
| 7 | 142 | 223 |
| 9 | 243 | 351 |
| 9 | 252 | 333 |
| 9 | 423 | 216 |
| 10 | 622 | 343 |
| 10 | 262 | 154 |
| 12 | 516 | 624 |
| 12 | 426 | 264 |
| 14 | 662 | 554 |
| 14 | 446 | 554 |
Thank you year 3/4 from St. Peter Julian Eymard