Three Digits
Imagine that you have 25 beads.
You have to make a three-digit number on an abacus.
You must use all 25 beads for each number you make.
Which of these numbers can you make?
178
799
386
209
What numbers can you not place in the hundreds column?
How many three digit numbers can you make?
answers
Add the digits up and compare with the number 25 which is the total number
of beads which must all be used.
178
799
386
209
no
yes
no
no
because
because
because
because
1
7
3
2
+
+
+
+
7
9
8
0
+
+
+
+
8
9
6
9
=
=
=
=
16
25
17
11
The maximum of the two digits in the tens and units column is 18 (9 + 9)
You cannot have the digits 1, 2, 3, 4, 5, or 6 in the hundreds column as the
remainder after taking the hundreds digit away from 25 is more than 18.
So the possible numbers are:799
889
979
898
997
988