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benachie
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My son who is at primary school was given the following homework:
"Finding all possibilities Logic Problem"
Jessica and Simon were blowing up balloons for Garreths birthday. There were at least two of each. Some balloons had three spots and some had 5 spots.
There were 31 spots altogether.
Q: How many balloons had three spots and how many had 5 spots?
What if there were 24 spots?
What if there were 65 spots?
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OK, so knowing that there were two of each to start with (5+5+3+3=16 spots) we only need to establish the possible permutations for the remaining 15 ie 3 x 5 spot balloons or 5 x 3 spot balloons
For 24 spots there is only one possible answer (24 - 16 = 8 spots = 1 x 5 spot balloon and 1 x 3 spot balloon
For 65 there are a few permutations 65-16=49
8 x 5 + 3 x 3 = 49
2 x 5 + 13 x 3 = 49
5 x 5 + 8 x 3 = 49
But can we be sure that we have found all the possible answers? Is there a formulae for testing and am I posting this question in the right place!
"Finding all possibilities Logic Problem"
Jessica and Simon were blowing up balloons for Garreths birthday. There were at least two of each. Some balloons had three spots and some had 5 spots.
There were 31 spots altogether.
Q: How many balloons had three spots and how many had 5 spots?
What if there were 24 spots?
What if there were 65 spots?
---------------------------------
OK, so knowing that there were two of each to start with (5+5+3+3=16 spots) we only need to establish the possible permutations for the remaining 15 ie 3 x 5 spot balloons or 5 x 3 spot balloons
For 24 spots there is only one possible answer (24 - 16 = 8 spots = 1 x 5 spot balloon and 1 x 3 spot balloon
For 65 there are a few permutations 65-16=49
8 x 5 + 3 x 3 = 49
2 x 5 + 13 x 3 = 49
5 x 5 + 8 x 3 = 49
But can we be sure that we have found all the possible answers? Is there a formulae for testing and am I posting this question in the right place!