I have 10 boxes and 44 marbles .Can I put my marbles in the boxes so that each box contains a different number of marbles?
That's what I got too !!! May be it's a trick question - Thank you for trying
Perhaps I am thick this afternon, but I can see how this can be done with 45 marbles but not 44.
0,1,2,3,4,5,6,7,8,9
which makes 45 marbles.
Yes, it is possible to put the 44 marbles in the 10 boxes such that each box contains a different number of marbles. Here's a step-by-step breakdown of how you can do it:
1. Start by putting 1 marble in the first box.
2. Then, put 2 marbles in the second box.
3. Continue this pattern, increasing the number of marbles in each box by 1, until you reach the ninth box. In other words, put 3 marbles in the third box, 4 marbles in the fourth box, and so on.
4. Now, you have used 1 + 2 + 3 + ... + 9 = 45 marbles across the first nine boxes.
5. Subtracting these 45 marbles from the total number of marbles (44 - 45 = -1), you are left with -1 marble.
6. Since we need to distribute all 44 marbles, we will need to redistribute one of the marbles from the previous boxes.
7. Choose any one of the first nine boxes and remove one marble from it. Let's say you remove a marble from the seventh box.
8. Now, distribute this removed marble among the remaining boxes. Each of the remaining boxes (10th box included) will get one more marble, making a total of 10 marbles distributed.
9. You now have 33 marbles distributed among the first nine boxes (1+2+3+4+5+6+8+9 = 38), and 10 marbles in the tenth box from the redistribution (1+1+1+1+1+1+1+1+1+1 = 10). This totals to 38 + 10 = 48 marbles.
10. As a result, each box now contains a different number of marbles, with the number of marbles ranging from 1 to 10.
So, by redistributing one marble, you can put 44 marbles in the 10 boxes so that each box contains a different number of marbles.
To determine if you can put the marbles in the boxes so that each box contains a different number of marbles, let's consider the different possibilities:
Since you have 10 boxes, the maximum number of different numbers of marbles you can distribute is 10. In the best-case scenario, each box would contain a different number of marbles from 1 to 10. However, you only have 44 marbles, which means some numbers will be repeated.
To check if it's possible, let's start by assuming the marbles will be distributed in increasing order of numbers, from 1 to 10. In this case, the total number of marbles would be the sum of all numbers from 1 to 10. The formula to calculate this sum is given by: S = (n * (n + 1)) / 2, where S represents the sum and n is the last number in the sequence (in this case, 10).
Using this formula, we find that the sum of marbles for 10 boxes is: S = (10 * (10 + 1)) / 2 = 55.
Since you only have 44 marbles, which is less than the sum of marbles for 10 boxes, it is not possible to distribute the marbles in the boxes so that each box contains a different number of marbles.
Therefore, it is not possible to put the marbles in the boxes as per the given condition.