- #1
julian
Gold Member
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I buy a packet of 28 biscuits with intention of eating two biscuits every lunch time (including weekends). However, sometimes I get greedy and eat an extra biscuit at lunch time (I always eat 2 or 3 biscuits each day). If I DONT eat any extra I would end up eating the last two biscuits on say a Thursday lunch time, and as such would have no biscuits left to eat on the Friday lunch time. Now say I did eat extra - question: how many extra biscuits have I eaten in order to have no biscuits left to eat Wednesday (in the second week) lunch time?
The answer is...if I get to Wednesday and find I don't have the two biscuits I was going to eat that lunch time and I don't have the two biscuits I was going to eat Thursday lunch time then I must have eaten 4 more than I should have, so the answer is 4 extra.
A person I know is saying I ate 6 extra biscuits (errh?). I try telling him that if I get to Wednesday and I'm missing 4 biscuits (the two for Wednesday lunch time and the two for Thursday lunch time) then I must have eaten 4 extra.
He can't work out why this is correct. How would you explain it to a person?
Here are a couple of arguments you can give:
Here is an argument that directly equates number of extra eaten to number left come Wednesday when sticking to two biscuits per day:
Here is something you would physically do:
See what arguments you would give...
The answer is...if I get to Wednesday and find I don't have the two biscuits I was going to eat that lunch time and I don't have the two biscuits I was going to eat Thursday lunch time then I must have eaten 4 more than I should have, so the answer is 4 extra.
A person I know is saying I ate 6 extra biscuits (errh?). I try telling him that if I get to Wednesday and I'm missing 4 biscuits (the two for Wednesday lunch time and the two for Thursday lunch time) then I must have eaten 4 extra.
He can't work out why this is correct. How would you explain it to a person?
Here are a couple of arguments you can give:
Here is an argument that directly equates number of extra eaten to number left come Wednesday when sticking to two biscuits per day:
On a certain number of lunch times I ate an extra biscuit so as to end up with none left to eat on the Wednesday (of the second week).
Here is something you can do...Do the whole over again but this time instead of eating the extra biscuit that you remove from the packet, place it to one side. You do this enough times in order to have none left in the packet come Wednesday. The number you have put to one side is then exactly equal to the number of extra biscuits I ate!
All we have to do now is work out how many biscuits I would put to one side, but that is easy...because I'm not eating the extra biscuits I take out of the packet, it means that I am eating two biscuits per day. But we know what happens when I stick to two biscuits per day, I end up with 4 biscuits left come Wednesday (two for Wednesday lunch time and two for Thursday lunch time). So 4 is the number I will have put to one side because that is how many I'm supposed to have left over. So 4 is the number of extra biscuits eaten.
Here is something you can do...Do the whole over again but this time instead of eating the extra biscuit that you remove from the packet, place it to one side. You do this enough times in order to have none left in the packet come Wednesday. The number you have put to one side is then exactly equal to the number of extra biscuits I ate!
All we have to do now is work out how many biscuits I would put to one side, but that is easy...because I'm not eating the extra biscuits I take out of the packet, it means that I am eating two biscuits per day. But we know what happens when I stick to two biscuits per day, I end up with 4 biscuits left come Wednesday (two for Wednesday lunch time and two for Thursday lunch time). So 4 is the number I will have put to one side because that is how many I'm supposed to have left over. So 4 is the number of extra biscuits eaten.
Here is something you would physically do:
Get 14 boxes. Label each box by a day of the week. Get your 28 biscuits and put two biscuits in each of these boxes - the last box being labelled the "Thursday of the 2nd week". When you want to eat an extra biscuit on one of the lunch times you draw from one of the biscuits in the "Thursday of the 2nd week" box. On another day when you want to eat an extra biscuit you draw from the one biscuit left in the "Thursday of the 2nd week" box. If you want to eat a 3rd extra you draw from one of the biscuits in the "Wednesday of the 2nd week" box. When you want to eat a 4th extra you draw from the one biscuit left in the "Wednesday of the 2nd week" box.
And then you stop eating any more extra biscuits because that would involve eating one of the biscuits in the"Tuesday 2nd week" box.
And then you stop eating any more extra biscuits because that would involve eating one of the biscuits in the"Tuesday 2nd week" box.
See what arguments you would give...