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What is the units digit for the number 123^(456) ?

Add 3 Dice

Stage: 2, 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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