Every year, many students across the UK take part in UKMT competitions, and problem solving rounds are one of the most talked-about parts. These rounds ask pupils to do more than just remember maths facts. They ask for clear thinking, careful reading, and steady focus under time pressure.
Still, we often see even confident pupils get stuck at the same points, not because they don’t know enough maths, but because certain question steps throw them off. These bits aren’t always large or obvious, they’re small details that sneak by and pull the problem off course. So let’s look at the common trouble spots in problem solving rounds and how spotting them early can help pupils get through more questions with more confidence.
Misreading What the Problem Is Actually Asking
Many pupils have the maths skills they need to handle the question, but they miss the real meaning of what is being asked. That could happen in the very first line, or toward the end, when they think they’ve solved it but haven’t answered fully.
• Words like “exactly,” “at most,” “at least,” and “how many different ways” can change what a pupil needs to find
• Some questions ask for all possible answers, while others only want one that meets a narrow condition
• A familiar setup might hide a different goal, and pupils who answer without double-checking what’s being asked often miss the mark
Reading carefully is key, yet under stress that’s the first habit many abandon.
Missing the Clue Hidden in the Early Steps
UKMT problems often have helpful hints built into the first couple of steps, but many pupils rush past these. It might be a pattern they don’t pause to notice, or two pieces of information that connect in a useful way.
• Some questions only start to make sense when you combine ideas from earlier steps
• If a number repeats or a shape flips in a certain way, that small clue can suggest the right approach
• Nervous pupils sometimes treat each part of the question like a new problem instead of stopping and asking what’s already been revealed
We often remind learners that working slowly in the first part of a problem can actually save time later. Jumping ahead can mean missing the doorway that was there the whole time.
Forgetting to Test an Answer or Check Back
It’s easy to feel the clock running and want to move on the second you have what feels like an answer. But many questions, especially in UKMT competitions, are built with edge cases. A pupil might miss a small detail that changes the number of answers or ask for a different kind of solution than what they worked out.
• Some problems have simple-looking answers that are wrong if you don’t test them
• Questions that ask for “how many ways” might mean the method is more important than the final number
• Pupils who don’t go back to the question at the end may miss the chance to fix tiny errors
A short moment of reviewing the final step is often all it takes to see what’s missing, and can be the difference between full marks and none at all.
Getting Lost in Working Without a Plan
When no obvious method jumps out, some pupils try a few random ideas just to get started. The problem is, this often leads to a messy patch of notes that doesn’t move forward.
• UKMT problems reward having a path, even if it’s not the shortest one
• Pupils who stop and try drawing something, listing examples, or writing what they do know often reconnect with the shape of the problem
• Those who skip this step sometimes circle around the same thoughts but don’t move through them
We find it helps to name what you do see, even if the full plan isn’t there yet. That way, your brain can more easily spot what’s missing.
Starting Too Fast Without Reading the Whole Question
Fast solving often comes at a cost. It’s tempting to race into a problem the moment it looks similar to something from practice. But many longer questions need a full scan before starting, especially ones with layered conditions.
• A careful read of the full text first can stop silly errors
• Questions are sometimes better tackled backward, starting from the thing you’re asked to find
• Pupils who pause and name the pieces they’ve been given often get clearer quicker, but those who rush tend to miss small shifts in meaning
We tell learners that in timed settings like these, faster isn’t always better. A clean first read saves more time than fast working on a wrong plan.
Building Confidence by Knowing the Tricky Spots
The truth is, these tripping points are normal. Most pupils struggle in the same places, and slipping up doesn’t mean the maths is out of reach. In fact, it often means a learner is stepping into a new kind of thinking, less about quick recall, and more about flexible problem solving.
• Recognising common tough steps helps pupils spot patterns in their own thinking
• Learning where the question tried to throw them off helps them not fall for the same move next time
• Struggling in these spots isn’t a weakness, it’s practice in motion
When pupils get used to slowing down at the right part of a question, they not only solve more, they feel stronger facing new ones. That comfort builds problem confidence bit by bit, and over time, the same questions that once felt impossible start to feel like fair puzzles they know how to face.
Unlock your child’s potential in UKMT competitions with tailored guidance from Learnfluid. Our expert tutors focus on building problem-solving skills and confidence by addressing common pitfalls and developing strong habits. With personalized support and innovative tools, we help students transform challenges into triumphs. Get in touch today and let us support your child’s journey to success.