How to Tackle Challenging Questions in the Senior Maths Challenge?

[david18]

Hi I am taking senior maths challenge this year and was looking over some of the past paper questions. I did the first 10 questions and they seemed okay (although i took a bit of time on the year question which turned out to be monday) and looked at q10.

http://www.wpr3.co.uk/UKMT/smc.html (scroll to q10)

Is there any method to tackle this kind of question? I could spend a lot of time experimenting with different numbers but I'm usually used to having some kind of method to go through the question. Any help on a good logical approach/method would be appreciated.

Thanks.

 

[CRGreathouse]

Well, you can start by noting that the leftmost column sums to 13 so the two empties sum to four. This forces one tow be 3 and the other to be 1, since duplication isn't allowed.

 

[Diffy]

CRGreathouse has the right method. Use the same logic on the bottom row (ie figure out which numbers HAVE to be used, and why). Then you should be left with three numbers that have not been used. From there, you need to think, what happens if the top column is 9 1 3 (descending), then whcih of my three numbers left would work (if any.. hint hint).

So the trick is, to assume that there is only one possible place for each of the nine numbers. If that is the case, you can work out deductively what has to go where.

 

[nesna]

I don't know if there is a shorter method than to use the process of elimination. I am not sure if it is possible that it might have more than one solution.

Anyways, it seems the sequence

9
3
1 8 4
* * 7
* * 2 6 5


works.

 

[david18]

yeah thanks alot, i worked the answer using the same idea as crg and diffy said and got the same answer as nesna.

Im not used to these kinds of questions as the national exam questions always have a strict method to follow.