You have 10 boxes and 44 marbles. Is it possible to put all of your marbles in the boxes in such a way that each box contains a different number of marbles?
No, in order to have a different number of marbles in each of the boxes you would need at least 55 marbles.
no
try with the smallest possible sum
1+2+3+4 ..
1+2+...+8+9 = 45
adding up the marbles in the first 9 boxes is 45, so we don't even have enough marbles to use the smallest numbers possible
To determine if it is possible to put all 44 marbles in 10 boxes in such a way that each box contains a different number of marbles, we can approach it by trying to distribute the marbles among the boxes in a way that satisfies the condition.
Since there are 10 boxes, we would ideally want to distribute the marbles in a way that each box contains a different number of marbles, ranging from 1 to 10 (to cover all the boxes). Therefore, we need to find a way to divide 44 into 10 distinct numbers.
We can start by considering the smallest number of marbles and distribute them evenly amongst the boxes. So, we can place 1 marble in the first box, 2 marbles in the second box, 3 marbles in the third box, and continue this pattern until the 9th box. However, since the 10th box would need to have more than 9 marbles, it would not satisfy our condition.
Let's try a different approach. We can distribute the marbles in a way that each box contains a different number of marbles, but not necessarily in a consecutive order. For example:
- Box 1: 4 marbles
- Box 2: 8 marbles
- Box 3: 12 marbles
- Box 4: 16 marbles
- Box 5: 20 marbles
- Box 6: 24 marbles
- Box 7: 28 marbles
- Box 8: 1 marble
- Box 9: 2 marbles
- Box 10: 5 marbles
In this case, each box contains a different number of marbles, and we have used all 44 marbles.
Therefore, it is possible to put all 44 marbles in the boxes in such a way that each box contains a different number of marbles.