Once again some great problem solving - sorry for the delay in getting this weeks problem on-line.
Last weeks answer:
Find a pattern.
2 steps 3 cubes 2 + 1
3 steps 6 cubes 3 + (2 + 1)
4 steps 10 cubes 4 + (3 + 2 + 1)
5 steps
9 steps 45 cubes 9 + (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1)
You will need 45 cubes.
This weeks problem:
An ice cream stand has nine different flavours. A group of children come to the stand and each buys a double scoop cone with two flavours of ice cream. If none of the children choose the same combination of flavours, and every different combination of flavors is chosen, how many children are there?
FLAVOURS
1 Vanilla
2 Maple
3 Chocolate
4 Tiger
5 Raspberry
6 Strawberry
7 Coffee
8 Moon Mist
9 Cherry Vanilla
Can the double scoop cones have 2 scoops the same flavour? I am not sure but I don't think they can. Please tell me!
ReplyDeleteFrom Billie
Hi,
ReplyDeleteWhat I did to solve this problem was this:
For the first scoop on the ice-cream there are nine possible choices. For each of the 9 different first scoops there were 8 possible choices for the second scoop because you aren't allowed to use the same flavour again.
So you can make 9x8=72 different double-scoop ice-creams. Each combination of flavours can be made in 2 ways.(flavour A followed by flavour B and flavour B followed by flavour A). So the number of different flavour combinations is 72 divided by 2=36.
From Alex.
I found out the answer by adding up all the combinations. i started with vanilla I could add 8 different flavours to the vanilla. then i started with maple i could only add seven flavours to the maple because i had already made a vanilla and maple ice-cream before. starting with chocolate i could only make 6 different ice-creams tiger 5 rasberry 4 strawberry 3 coffee 2 and moon mist 1.i could not add any more flavours to cherry vanilla. the total number of different ice-creams is 8+7+6+5+4+3+2+1. i added pairs of compatible numbers adding to 10 there were 3 pairs and the numbers 5&1 were left over & I added them on. My answer is 36!
ReplyDeleteFrom Kate
Hi Billie
ReplyDeleteEach scoop has to be a different flavour so you can't have an ice cream that has 2 scoops of the same flavour.
A good question!
I worked out the problem like this.
ReplyDeleteI drew 9 circles to show different flavours. I then drew two circles together with the first numbers 1 and 2 inside them to show the 1st kids icecream flavours. I drew two more circles for the 2nd kid with the numbers 1 and 3 inside them for the flavours. I found that there were 8 kids that had the flavour 1 in their icecream. I counted that 7 kids had flavour 2 with the other flavours. I kept drawing the kids with two circles all the way up to flavour 9 and then I found out that there were 36 kids that got icecreams.
I love these problems. Thankyou Mrs Cope.
From Mia
I think there are 36 combinations. I worked it out by writing down:V(vanilla)+M(maple)etc. etc. until I had all the combinations. Than I counted the combinations up. Thats how I got 36.
ReplyDelete-Billie