Helen and Ivan Coin Question Solution: A Step-by-Step Breakdown

Quick Answer: The Helen and Ivan coin question is solved by applying the comparison heuristic — recognise that both children hold the same total number of coins, so the difference between their coin collections (and thus the difference in total mass) comes entirely from the different number of heavier versus lighter coins. The key insight is that you do not need to calculate every individual value; you only need to compare the differing parts.

This walkthrough breaks the solution into clear steps, explains the reasoning behind each one, and highlights the common pitfalls that cause students to go wrong. Whether you are a parent trying to understand what your child faces or a student reviewing problem-solving techniques, this guide should make the logic clear.

The Helen and Ivan coin question solution uses the mathematical principle that when two sets share identical components, the difference between the sets depends only on the components that differ — a comparison heuristic taught throughout the MOE primary math curriculum.

Step 1: Understand What the Question Gives You

The problem presents two children, Helen and Ivan, each holding a collection of coins of two types. Both children have the same total number of coins. You are told how many of each coin type Helen has, how many of each type Ivan has, the known total mass of the coins one child holds, and the mass difference between the two coin types.

The first reaction many students have — and many parents had when the question went viral — is to try to calculate the exact mass of each coin type individually and then compute everything from scratch. This approach is not wrong in principle, but it is inefficient and error-prone under exam time pressure. The better approach is to compare, not calculate.

Step 2: Apply the Comparison Heuristic

Since Helen and Ivan have the same total number of coins, any difference between their collections must be symmetrical: for every extra heavier coin one child has, they have one fewer lighter coin. This means the mass difference between their total collections is simply the number of extra heavier coins multiplied by the mass difference between one heavier and one lighter coin.

In mathematical language: mass difference = (difference in number of heavier coins) × (mass per heavier coin − mass per lighter coin). The common coins — the coins of each type that both children hold in equal numbers — contribute equally to both children's total mass and cancel out when you subtract. This is the insight that makes the problem straightforward.

Step 3: Answer Part (a) — Who Has More Money

The question about who has more money is the simpler of the two parts. If the heavier coin is also the more valuable coin — as is typically given in the problem — then the child with more of the heavier coins has more money. Count the heavier coins each child holds, compare, and state which child has more, with the difference in coin count multiplied by the value difference as supporting reasoning.

Step 4: Answer Part (b) — The Mass Difference

Using the comparison heuristic from Step 2, calculate the number of extra heavier coins one child has over the other. Multiply this number by the given mass difference between one heavier coin and one lighter coin. The result is the mass difference between the two children's total coin collections.

This step should take no more than two to three lines of working if the student has correctly identified the heuristic. Students who fill a page with dense calculations are likely trying to solve the problem by brute force, which is where mistakes creep in.

Common Mistakes Students Make

The most frequent error is treating the problem as a pair of simultaneous equations and attempting to solve for the mass of each coin type individually. While mathematically possible, this approach is unnecessarily complex and often leads to arithmetic errors. Another common mistake is misreading which child has more of which coin type and producing a sign error (getting the direction of the difference reversed).

A subtler error is failing to state the reasoning clearly. PSLE markers award marks for method, not just the final answer. A student who writes "Helen has 20 more 20-cent coins, at 3g more per coin, so her coins are 60g heavier" gets full marks. A student who writes "60g" with no working may lose method marks even if the answer is correct.

How to Practise Problem-Solving Skills

The best preparation for heuristic-based questions is exposure to variety, not repetition of the same format. Students should practise identifying which heuristic applies to which question type — comparison, working backwards, guess and check, drawing a model, making a list, and so on — because PSLE Math papers increasingly mix these within a single paper.

English reading comprehension plays an underappreciated role in math problem-solving. Students who misread a word problem because they skimmed a key phrase — "the same total number of coins" is the pivotal phrase in the Helen and Ivan question — will get the answer wrong regardless of their mathematical ability. iWorld Learning's PSLE English programmes strengthen the precise reading skills that support accurate problem interpretation across all subjects.

FAQ

Could the question be solved using algebra?

Yes, but the MOE primary syllabus does not formally teach algebra as a problem-solving method. Primary students are expected to use heuristics — model drawing, comparison, working backwards — rather than algebraic notation. A solution using variables and simultaneous equations would be technically correct but would show that the student used a method outside the intended primary curriculum.

How many marks was the question worth?

The question was reported to be worth four to five marks in total, split between the two parts. In the context of the full PSLE Math paper, it was a high-value question — getting it right could meaningfully affect the overall Math AL grade. This is why the question attracted so much attention: it was both conceptually tricky and heavily weighted.

What should a parent do if their child is stuck on similar questions?

First, ask the child to explain what they think the question is asking. Often, the block is in reading comprehension, not mathematics. Second, guide them to identify what is the same and what is different between the two scenarios — this "compare and contrast" framing unlocks most heuristic-based problems. Third, resist the urge to solve it for them. The skill being tested is problem-solving independence, and children build that skill through guided struggle, not through being shown the answer.

Are there other PSLE questions like this that went viral?

PSLE Math questions periodically capture public attention when they appear unusually difficult at first glance. Examples include the "ribbon" question (2017), the "pattern-spotting" question (2019), and various "angle-finding" geometry questions over the years. Each viral question typically tests a heuristic rather than advanced content, and each triggers a similar cycle of public concern followed by MOE clarification that the question was within syllabus.

Summary

The Helen and Ivan coin question is solved elegantly — and quickly — with the comparison heuristic: ignore what is the same, focus on what is different, and multiply the difference in quantity by the difference in mass. The question rewards students who have internalised heuristic-based problem-solving, not those who rely on rote procedures. For parents supporting P6 students, strong English comprehension is an essential foundation for accurate math problem interpretation. iWorld Learning's PSLE English programmes at Tanjong Pagar and Somerset build this foundational skill. Contact us to learn more.