Asmo is putting some ping pong balls into 10 boxes. In each of the boxes,
number of ping pong balls shall not be less than 11, not equal to 17 and is
not the multiple of 6. If the number of ping pong balls are different in each
box, at least how many ping pong balls for Asmo to fill in all the 10 boxes?
allowed numbers: 11,13,14,15,16,19,20,21,22,23
add them up
thank you!
To find the minimum number of ping pong balls that Asmo needs to fill all 10 boxes, we need to consider the conditions given:
1. The number of ping pong balls in each box should not be less than 11.
2. The number of ping pong balls in each box should not be equal to 17.
3. The number of ping pong balls in each box should not be a multiple of 6.
4. The number of ping pong balls in each box should be different.
Let's break down the conditions one by one to determine the minimum number of ping pong balls needed:
1. The number of ping pong balls in each box should not be less than 11.
This means that the minimum number of ping pong balls in each box should be 11.
2. The number of ping pong balls in each box should not be equal to 17.
This means that 17 is not allowed as a number of ping pong balls in any of the boxes.
3. The number of ping pong balls in each box should not be a multiple of 6.
This eliminates numbers like 6, 12, 18, etc., as they are multiples of 6.
4. The number of ping pong balls in each box should be different.
This condition means that no two boxes can have the same number of ping pong balls.
To find the minimum number of ping pong balls, we need to consider the conditions that result in the smallest possible numbers for each box. Asmo needs to assign different numbers of ping pong balls to each of the 10 boxes, starting from the minimum value of 11 and increasing by 1 for each box.
Here is a possible distribution of ping pong balls for Asmo to fill all 10 boxes:
Box 1: 11 ping pong balls
Box 2: 12 ping pong balls
Box 3: 13 ping pong balls
Box 4: 14 ping pong balls
Box 5: 15 ping pong balls
Box 6: 16 ping pong balls
Box 7: 19 ping pong balls
Box 8: 20 ping pong balls
Box 9: 21 ping pong balls
Box 10: 22 ping pong balls
In this distribution, no two boxes have the same number of ping pong balls, the numbers are greater than 11 (the minimum allowed value), and they are not multiples of 6. Asmo would need a minimum of 22 ping pong balls to fill all 10 boxes.