Copyright © University of Cambridge. All rights reserved.
'(w)holy Numbers' printed from http://nrich.maths.org/
Chris and Matt at Staunton and Corse School
You would need 81 small boards made up of:
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 hymn 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 hymns 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