Sums using 9 digits! - Addition

Introduction

Directions: Using all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) once, in each box to make a sum as large as possible.

Hint:

Think about where you put the largest digits to get the largest values.
Try it and see. For each try, you will probably learn how to adjust and make it better.

Directions: Using all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) once, in each box to make a sum as small as possible.

Hint:

Think about where you put the smallest digits to get the smallest values.
Try it and see. For each try, you will probably learn how to adjust and make it better.

Directions: Using all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) once, in each box to make a sum as close to 1,000 as possible.

Hint:

Start with a guess. Like 123 + 456 + 789. Check and adjust.
Consider what to put in the hundreds place to add to 900, then adjust the other places with the digits you have left.

Directions: Using all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) once, in each box to make a sum

Hint:

Moving digits reviews place value and addition.

Least possible sum is 774.
Greatest possible sum is 2,556
Can you prove it isn't possible to get 1,000?
If you had a 0 as a digit to use, would it be possible?
What is the closest number to 1,000 that is above 1,000that the 9 digits will add to?
If we add all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) we get 45.
45 is a multiple of 9. ∴ any sum of all nine digits will be a multiple of nine.
1,000 isn't a multiple of nine. Check out multiple & factors.
Multiples of nine ... 990, 999, 1,008, ...
There are 180 unordered ways to add to 999. (two ways to add to 8 in the hundreds place, ___ ways to add to 18 in the tens place, and ___ ways to add to 19 in the ones place. There are five ways to organize digit for the 8-18-19 pattern and 36 ways to organize these three digit numbers for each of these five.

Conjecture 1. There is no combination of numbers using all the digits 1 to 9 (1 ,2, 3, 4,5, 6, 7, 8, 9) that will sum to 1,000.