DIY Challenge 2: Three groups of nine
Look at all the ways that we have found for making 3 groups of 9 cards.
What are some observations you can make? Why do think that is happening? An example is shown below. Come up with as many observations as you can.
| Observation | Possible Reason |
|---|---|
| Sum of numbers in each group is 15 | Sum from 1 to 9 is 45. Three equal groups will mean 45 divided by 3, which is 15. |
| 9 and 8 are never in the same group. | ? |
| …… | |
| …… |
What students worked out7
Student 10
Sir, 1 and 2 cannot come in the same group.
Reason:
1+2 = 3.
Therefore, to make the sum of the cards 15, the 3rd card we will need will be (15-3) which is 12, and we don’t have it. The card with most value available to us is 9.A card with the value of 5 at least is necessary, if one of the other two cards is 1.
Student 2
they can 1/2/3/4/5 or 1/2/3/9 or 1/2/5/7 or 1/2/4/8
Student 4
If we are to divide 9 cards into 3 groups, with every group having an equal total sum of cards, we need to add numbers one to nine and divide the total by three. If we do so, we get 15 as the total of each group of cards. If we group nine and eight, the sum of the two cards would be 17. So the other groups would have to have 9 as the total. That would make the groups unequal, and we can’t make two groups each adding up to nine with the cards we have left over
Student 3
8 and 9 can not come together because total is 17
similarly 9 and 7 can not come
as total is 16Student 6
8 and nine cannot come in a same group as it total becomes 17,
as it becomes unequal, and we can’t make two groups each adding up to nine with the cards we have left over.Student 2
8/9 and 7/9 can never be in the same group
Student 5
8/9 and 7/9 can not be in the same group cause 8/9 make 17
similarly, 7/9 make 16