2. Card games An Investigation

3. Peter, Alan and Shirley are playing a game using the 9 cards shown below. The cards are turned over and mixed up, so that no one knows which card is which. Each player in turn picks up a card until they each have 3 cards and all 9 cards have been picked up. The players then add up the numbers on their own cards. 2 2 1 33456 7

4. Peter gets a total of 14. "You must have picked up cards with the numbers 7, 6 and 1 “, Alan said to Peter. “ Not necessarily ", said Peter, “it could have been cards numbered with 6, 5 and 3. INVESTIGATE and find all the different ways that the 9 cards can be picked up so that Peter has a total of 14 Alan has a total of 11 and Shirley has a total of 8.

5. Repeat the above example for the situation below. INVESTIGATE and find all the different ways that the 9 cards can be picked up so that Tom has a total of 12, Dick has a total of 10 and Harry has a total of 8. 1 2 1 2 4 6 4 55 Tom, Dick and Harry are playing a game using the nine cards shown

6. David, Elizabeth and Aimee' are playing a game using the 9 cards shown 2 53 2 3 4 1 4 1 INVESTIGATE and find all the different ways that the 9 cards can be picked up so that David has a total of 10, Elizabeth has a total of 8 and Aimee' has a total of 7.

7. Solution Solution to 14-11-8 :- the possibilities are listed in the table below 761 542 332 761 533 422 752 641 332 752 632 431 743 632 521 653 731 422 653 722 431

8. Solution 12-10-8 :- the possibilities are listed in the table below 651 541 422 651 442 521 642 541 521 552 442 611

9. Solution Solution to 10-8-7 :- the possibilities are listed in the table below 541 422 331 541 431 322 541 332 421 532 431 421 442 521 331 442 332 511 433 521 421 433 422 511