Question

What do the digits in the number 15 add up to? Answer 1+5=___.
Using single digits, how many different ways can you add up to 6?.

Example:
The least number of digits is 2, and it is 1+5=6. The greatest number of digits is 6, and it is 1+1+1+1+1+1=6.

1.How many other numbers have digits with the same total 6, if we only include numbers without zeros?___
2.What is the total number of ways you can arrange a sum of 6?____

Hint:Do your work in a logical way,i.e. start off with using only 2 digits, then 3,then 4 and so on.

Answer 1

One digit numbers: 6 (one possibility only)

Two digit non-zero numbers:
15, 24, 33, 42 and 51 (total = 5)

Three digit numbers:
123, 213, 132, 312, 321, 231
114, 411, 141, 222 (total = 10)

Four digit numbers:
1113, 1131, 1311, 3111
1221, 2121, 1122, 2211
2112, 1212 (total = 10)

Five digit numbers:
11112, 11121, 11211, 12111, 21111
(5 numbers)

Six digit numbers: 111111 (one only)
Total number of possibile arrangements = 32 (without using zero)

Sum of 1: One possibility (1)
Sum of 2: Two possibilites (2,11)
Sum of 3: Four possibilities
(111, 12, 21, 3)
Sum of 4: (Eight possibilities.
(4, 13, 31, 22, 112, 121, 211, 1111)
Thus for a sum of five there are 16 possibilities.
For a sum of N there are 2^(N-1) possibilities.

Answer 2

How to solve x+7y=8 8x-4y=-2