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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