Fifteen Cards
For this question, there are 2 possible answers. My possible answers are: 8, 7, 13, 10, 6, 12, 9 and 6, 9, 11, 12, 4, 14, 7. For this question, on rule is that the only numbers that are allowed are 1-15 and another rule is that numbers cannot be repeated. This is how I found the possible answers for this question. My strategies that I used were Guess and Check and Make a List.
The first clue is:'The numbers on the first 2 cards add up to 15.' I listed all the possible answers that add up to 15. These are all the formulas that add up to 15 (that are the numbers 1-15):
1+14, 2+13, 3+12, 4+11, 5+10, 6+9, 7+8, 8+7, 9+6, 10+5, 11+4, 12+3, 13+2, 14+1
The second clue is:'The numbers on the second and third cards add up to 20.' I listed all the possible answers that add up to 20. These are all the formulas that add up to 20 (that are the numbers 1-15):
5+15, 6+14, 7+13, 8+12, 9+11, 11+9, 12+8, 13+7, 14+6, 15+5
The third clue is:'The numbers on the third and fourth cards add to 23.' I listed all the possible answers that add up to 23. These are all the formulas that add up to 23 (that are the numbers 1-15):
5+18, 6+17, 7+16, 8+15, 9+14, 10+13, 11+12, 12+11, 13+10, 14+9, 15+8
The forth clue is:'The numbers on the forth and fifth cards add up to 16.' I listed all the possible answers that add up to 16. These are all the formulas that add up to 16 (that are the numbers 1-15):
1+15, 2+14, 3+13, 4+12, 5+11, 6+10, 7+9, 9+,7, 10+6, 5+11, 12+4, 3+13, 2+14, 15+1
The fifth clue is:'The numbers on the fifth and sixth cards add up to 18.' I listed all the possible answers that add up to 18. These are all the formulas that add up to 18 (that are the numbers 1-15):
3+15, 4+14, 5+13, 6+12, 7+11, 8+10, 10+8, 11+7, 12+6, 13+5, 14+4, 15+3
The last clue is' The numbers on the sixth and seventh cards add up to 21' I listed all the possible answers that add up to 21. These are all the formulas that add up to 21 (that are the numbers 1-15):
6+15, 7+14, 8+13, 9+12, 10+11, 11+10, 12+9, 13+8, 14+7, 15+6
The next step is to combine all the formulas together and use the strategy Guess and Check.