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Official TSR Mathematical Society

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Reply 980
rupertj
2/Actually, 2+2=4 is true, which was easy for me to realise as true since i don't know any computer science. Therefore, out of the remaining people, one must be telling the truth.


You have made an error in assuming it is true. Do you know what another base is?
DeanK2
You have made an error in assuming it is true. Do you know what another base is?


so am i right in assuming my answer is correct and before everyone else has assumed 2+2 = 4 is true they are wrong?

i only know because in year 9 my teacher asked us to tell her one thing which we knew to be 100% true so i said 1+1 = 2 and she showed me using a clock as an example that i was wrong ^_^
Reply 982
Chaoslord
so am i right in assuming my answer is correct and before everyone else has assumed 2+2 = 4 is true they are wrong?

i only know because in year 9 my teacher asked us to tell her one thing which we knew to be 100% true so i said 1+1 = 2 and she showed me using a clock as an example that i was wrong ^_^


You do have a foolproof logical argument.
Reply 983
rupertj
2/Actually, 2+2=4 is true, which was easy for me to realise as true since i don't know any computer science. Therefore, out of the remaining people, one must be telling the truth.


how does doing computer science make you realise that 2 + 2 = 4 is false?
Reply 984
DeanK2
You have made an error in assuming it is true. Do you know what another base is?

I do realise that I couldn't have assumed it, but after you said this I checked the mark scheme, according to which "Dianne is clearly telling the truth". Apparently the mark scheme expects you to assume it.

DeanK2
how does doing computer science make you realise that 2 + 2 = 4 is false?

I meant not knowing what mod 3 is rather than computer science itself (I'm not very far in my studies).
Reply 985
That is the one time those papers have been disspointing in terms of answers. Ofcourse it would have been ambiguous but having two possibilities for that question is clearly valid.
DeanK2
That is the one time those papers have been disspointing in terms of answers. Ofcourse it would have been ambiguous but having two possibilities for that question is clearly valid.


meh looks like we over complicated the question

but iunno i think if you wrote down, not in mod 3 they'd have to give you the marks
Dystopia
How about ?

And if you manage that one, then just change the 2 to a 3. :wink:

Comment: I can think of a few ways of evaluating this integral, but none of them are particularly pleasant or simple.

Anyone going to have a crack at my previous question?


Btw are you sure this converges?
Dadeyemi
people seem to be ignoring this, here's my quick stab at it

Spoiler



I know little of modular arithmetic, but there are more solutions.
Reply 989
Glutamic Acid
I know little of modular arithmetic, but there are more solutions.


What is your method... (please)
DeanK2
What is your method... (please)


Spoiler

Reply 991
3(b+1)(c+1) = 4bc -> bc - 3b - 3c = 0. Try factorizing, and you can find b and c. Rinse and repeat for different values of a.

I am very very tired but I do not think this is true.

3(c+1)(b+1) = 4bc --> bc - 3c - 3b - 3 = 0
Dadeyemi
Btw are you sure this converges?


Calculator says 2.064798 for the ^2 case :smile:

(and -6.04174 for the ^3 case)

Good incase anyone want to check their answers anyway...
DeanK2
3(b+1)(c+1) = 4bc -> bc - 3b - 3c = 0. Try factorizing, and you can find b and c. Rinse and repeat for different values of a.

I am very very tired but I do not think this is true.

3(c+1)(b+1) = 4bc --> bc - 3c - 3b - 3 = 0


Yes, you're right, it's late. But the method works.
Reply 994
Glutamic Acid
Yes, you're right, it's late. But the method works.


Sorry, the post referred to the expansion of 3(b+1)(c+1) which is incorrect in your spoiler.

However, I am not convinced there is a solution for a=2;
DeanK2
Sorry, the post referred to the expansion of 3(b+1)(c+1) which is incorrect in your spoiler.

However, I am not convinced there is a solution for a=2;


Spoiler

Reply 996
Glutamic Acid

Spoiler



Have you verified these? [When]

edit; my bad i pressed the wrong key.
Re cuboids:

There are 3 solutions with smallest side 2.
There are 2 solutions with smallest side 3.
Glutamic Acid
Yes, you're right, it's late. But the method works.


How would you go about finding all the solutions with this method though?
Dadeyemi
people seem to be ignoring this, here's my quick stab at it


=>(b+1)(c+1)=0 (mod a),(*) and similarly for b and c.
thus we can say WLOG b+1 = 0 (mod a)This isn't true. (e.g. 4.6 = 0 mod 12).

In practical terms, this problem is reasonably easy to solve by trial and error. If a<=b<=c, first assume a=2 and solve, then a=3. Finally, show there's no solutions if a > 3.

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