Song book

Chris and Matt at Staunton and Corse School told us:

You would need 81 digit cards made up of:

eight 0s

nine 1s

nine 2s

nine 3s

nine 4s

nine 5s

twelve 6s

eight 7s

eight 8s

They offered a good explanation for this. Beh Sze at Garden International School also explained carefully how he arrived at the answer:

0s - There can only be two zeros in each row because there is no 000 or 1000 in the song book.

1-5 - There can only be one triple digit number repeating the same single digit three times (e.g. 111, 222, 333). The rest can only repeat it twice at most (e.g. 011, 110, 101, 211, 311) because the numbers 111, 222, etc. cannot be repeated.

6s - Even though there cannot be a triple digit that repeats 6 three times, the extra 6s would be needed to be turned in to 9s (e.g. 696, 669, 699, 996). You must not forget that 6s can be turned into 9s.

7 and 8 - There can only be two, at maximum, of this number in each row (e.g. 177, 277, 377, 477, 070, 007). There cannot be 777 or 888 because the songs only stop at 700.

9s - 9 would work like 7 and 8 because it too cannot be written as 999. But the 9s do not need their own numbers because the numbers for 6 can be turned around to make 9.

Well done too to James and Jasmine at Old Earth Primary School who also reasoned through their solution very clearly.