Maths puzzle questions.
I'm unsure about some of the questions in this maths puzzle homework.
Here is one example of them I have already did without trouble.
Rules: Choose different combinations of baskets without taking mushrooms from the baskets to make a total of mushrooms in each question e.g 1-11, 1-6 etc.
Q.1 Suppose that there were four pigs with a basket each (B1, B2, B3 nad B4) and they brought back eleven mushrooms. Arrange the mushrooms in the baskets so that any total of mushrooms can be made from 1 to 11.
(note:for every question it is not allowed to remove mushrooms from baskets to help make up the totals).
I had to write out different combinations and each combination had to equal 11.
B1 1 1 1 1 1 1 1 1
B2 1 1 1 1 2 2 2 3
B3 4 3 2 8 3 4 6 3
B4 5 6 7 1 5 4 4 4
all add up to 11
The correct combination is
1 mushroom: select basket 1 or 2
2 mushrooms: Select basket 1 and 2
3 mushrooms: Select basket 3
4 mushrooms: select basket 3 and basket 1 OR 2
5 mushrooms: select basket 1, basket 2 and basket 3
6 mushrooms: select basket 4
7 mushrooms: select basket 4 and basket 1 or 2
8 mushrooms: select basket 4, basket 2 and basket 1
9 mushrooms: select basket 4 and basket 3
10 mushrooms: select basket 4, basket 3 and basket 1 OR 2.
11 mushrooms: Basket 1, basket 2, basket 3 and basket 4.
I think thats how you do it however there is a question I'm not sure with thats after the above question.
Question 2:Continue with the 4 basket situation and keep adding mushrooms. What is the maximum number of mushrooms which can be accommodated in four baskets and still allow all the totals to be made up?
Well I continued on with the same process as above until I got 16. So the the maximum number was 15 mushrroms becaue there were no combinations to complete the total of numbers for 16 with four baskets.
In one of the previous questions this had a similir quesiton and 7 mushrooms with 3 baskets was the limit because 8 didn't have a combination to complete the total of numbers 1-8.
Am I correct about this question.
There is another question I got to ask is there in another way to do it quicker or easier because I am up to the second last question which will take alot of time doing the above process.
Q.3 You should have discovered that there is a limit to the number of mushrroms which can be accomodated in four baskets. Try 5 baskets now to accomodate more mushrooms. What is the maximum number of mushrooms which can be accommodated in five baskets and still alllow all of the totals to be made up.
I have started writing combinations but I'm predicting it will be 23 is the maximum because the number without combinations to allow the totals to be made up go up in multiples of 8 I think so 24 musrooms work with 5 baskets I think.
But the writing the heaps of combinations there must be a another and it is consuming alot of my homework time, please help me with this question.
sorry for the long post