1. Sum Things Missing ! Let’s Play Sum Things Missing ! Rules: The Clue (dark box) is the Sum of the Digits (white boxes) Only use Digits 1 thru 9 (no 0) Duplicate Digits are Not Allowed The Digits can be in any Order

2. The Clue in the dark box is the Sum of the white box Digits When only one digit is missing, it’s easy to find the other. The Clue below is 6, 5 is already known. What digit is needed? Subtract 5 from 6 to find it. 6 – 5 = 1 The Clue below is 5, and both digits are missing. Possibilities? 1 + 4 will work, but so will 2 + 3 How about when the Clue is 4? Clue Use the Clue to figure out the Digits needed. Rules: -The Clue is the Sum of the Digits -Only use Digits 1 thru 9 (no 0) -Don’t Duplicate Digits -The Digits can be in any Order

3. Missing one digit? Just subtract the other two from the Clue. one at a time 11 – 3 – 2 = 6 or after summing 11 – (3 + 2) = 6 Missing 2 digits? Subtract the ones you know, then try possible combinations. 22 – 6 = 16 only two ways will work 8 + 8 are duplicates, must be 7 + 9 Often, there are several good combinations. For now, list them all. 11 – 3 = 8 so, good: 1+7, 2+6 bad: 3+5, 4+4 Try this one When the Sums get longer... Rules: -The Clue is the Sum of the Digits -Only use Digits 1 thru 9 (no 0) -Don’t Duplicate Digits -The Digits can be in any Order

4. Some Clues that are Sure Things – only one combination exists. The Number of Digits in the Sum is important, call it the Length. For each Length, there are 2 Minimums and 2 Maximums: Length 2 Min’s: L 2 Min’s: 3 and 4 Length 2 Max’s: L 2 Max’s: 17 and 16 You try… Length 3 Min’s: L 3 Min’s: 6 and 7 Length 3 Max’s: L 3 Max’s: 24 and 23 Try the smallest L 5 Minimum: What are the Digits? Then, the Clue. CluesSure Things Finding the Clues that are Sure Things. Rules: -The Clue is the Sum of the Digits -Only use Digits 1 thru 9 (no 0) -Don’t Duplicate Digits -The Digits can be in any Order

5. Possible Clues for Length 2 Sums. 3 3 – 1+2 (1 combination) Sure Thing 4 4 – 1+3 (1 combination) Sure Thing 5 – 1+4, 2+3 (2 combinations) 6 – 1+5, 2+4 (2 combinations) 7 – 1+6, 2+5, 3+4 (3 combinations) 8 – 1+7, 2+6, 3+5 (3 combinations) 9 – 1+8, 2+7, 3+6, 4+5 (4 combinations) 104+6Midway 10 – 1+9, 2+8, 3+7, 4+6 (4 combinations) Midway 11 – 2+9, 3+8, 4+7, 5+6 (4 combinations) 12 – 3+9, 4+8, 5+7 (3 combinations) 13 – 4+9, 5+8, 6+7 (3 combinations) 14 – 5+9, 6+8 (2 combinations) 15 – 6+9, 7+8 (2 combinations) 16 16 – 7+9 (1 combination) Sure Thing 17 17 – 8+9 (1 combination) Sure Thing Midway Clues are exactly between Min and Max For Length 2, 10 is Midway between 3 and 17 – 4+6 3+7 2+8 1+9 are valid combinations. For Length 5, 25 is Midway between 15 and 35 – Here are the 12 combinations that add up to 25 The Good News: No need to memorize them all! A Help Table will be provided. CluesSure Things Finding Digit Combo’s for Clues that are Between Sure Things. ? Possible Clues for Length 5 Sums. 15 15 – 1+2+3+4+5 (1 combo) Sure Thing 16 16 – 1+2+3+4+6 (1 combo) Sure Thing 17 – 1+…+7 (2 combo’s) 18 – 1+…+8 (3 combo’s) 19 – 1+…+9 (5 combo’s) 20 – 1+…+9 (6 combo’s) 21 – 1+…+9 (7 combo’s) 22 – 1+…+9 (9 combo’s) 23 – 1+…+9 (11 combo’s) 24 – 1+…+9 (11 combo’s) 253+4+5+6+7Midway 25 – 3+4+5+6+7 (12 combo’s)Midway 26 – 1+…+9 (11 combo’s) 27 – 1+…+9 (11 combo’s) 28 – 1+…+9 (9 combo’s) 29 – 1+…+9 (7 combo’s) 30 – 1+…+9 (6 combo’s) 31 – 1+…+9 (5 combo’s) 32 – 2+…+9 (3 combo’s) 33 – 3+…+9 (2 combo’s) 34 34 – 4+6+7+8+9 (1 combo) Sure Thing 35 35 – 5+6+7+8+9 (1 combo) Sure Thing ?

6. Each sum length from 2 thru 7 has Min and Max Clues that have only one valid combination of Digits. Each Clue between the Min and Max will have from 2 to 10 different combinations. The Midway Clues will have the most combinations. Here’s a summary: Let’s use 10 for a 2-digit sum as an example: – 4+6 3+7 2+8 1+9 are valid combinations. Let’s use 15 for a 3-digit sum. Valid combinations are: – 4+5+6 3+5+7 2+5+8 1+5+9 3+4+8 2+6+7 1+6+8 How about some Extra Credit? Even more XC: Play MrV’s Kardkuro Game in the LRCMrV’s Kardkuro Game

7. Cross-Sums Puzzles ! Let’s Examine Cross-Sums Puzzles ! Rules: The Clue (dark box) is the Sum of the Digits (white boxes) Only use Digits 1 thru 9 (no 0) Duplicate Digits are Not Allowed The Digits must be in Precise Order

8. Give these a try: Look for Clues that are Sure Things – only one combination exists: Sums can also be shown in a Vertical form. Rules: -The Clue is the Sum of the Digits -Only use Digits 1 thru 9 (no 0) -Don’t Duplicate Digits -The Digits can be in any Order

9. We have seen examples of Across-Sums and Down-Sums… When they are combined, they must Share a common digit. From now on, the Order of digits will matter. Use both Clues to determine their common digit in this puzzle: 4 can be 1 + 3 or 3 + 1 3 can be 1 + 2 or 2 + 1 The only digit common to 4 and 3 is 1 First: put in the common digit, 1 Then: Fill up 4 across. Put in 3 Then: Fill up 3 down. Put in 2 Solving Cross-Sums Puzzles. Rules: -The Clue is the Sum of the Digits -Only use digits 1 thru 9 (no 0) -Don’t duplicate digits -Order of digits now matters

10. When the puzzles get harder, look for the Sure Things first. – A Sure Thing is a Clue whose digits can only be one combination. 9 and 8 have lots of combinations, but 23 (length 3) is a sure thing. 23 must have digits 6, 8 and 9 then 9 could be 6 + 3 or 8 + 1 but 8 can only be 2 (top) + 6 (bottom) so start with 8… First: For 8, put in the 2 (top) + 6 (bottom) combination, Now: 9 has to be 8 (top) + 1 (bottom) And: Finish off 23 with 9 (middle) Cross-Sums Puzzles – Finding a Starting Place Rules: -The Clue is the Sum of the Digits -Only use digits 1 thru 9 (no 0) -Don’t duplicate digits -Order of digits now matters