Worked solution · PSLE 2021 Paper 2 Q15
The Helen and Ivan PSLE question, shown working
Parents still search for this one years later, and I understand why: it looks like a coins puzzle, but it turns on a single quiet idea most children read straight past.
Mrs Eileen Toh
Founder & Curriculum Architect · ex-MOE · 5 min read · Updated 22 Jun 2026
Some PSLE questions take on a life of their own, and the Helen and Ivan coins problem from the 2021 Paper 2 is one of them. Parents bring it to me long after the exam, partly because it reads as if it needs a great deal of arithmetic, and partly because the printed solution can feel like a string of numbers with no story. So let me show the working slowly, the way I would at the table, and then name the one idea that turns the whole thing into a short, calm piece of reasoning.
The question · 2021 Paper 2 Q15
Helen and Ivan have the same total number of coins. Helen has a number of fifty-cent coins and 64 twenty-cent coins. The total mass of her coins is 1.134 kg. Ivan has a number of fifty-cent coins and 104 twenty-cent coins.
(a) Who has more money, and how much more?
(b) Each fifty-cent coin is 2.7 g heavier than each twenty-cent coin. What is the total mass of Ivan's coins in kg?
We reproduce this question because it became national news — the famous “Helen and Ivan” coins question, covered by Mothership. For other questions our pages point you to your Ten-Year Series instead.
The one idea that unlocks it
Read the first sentence again, because it is doing all the work: Helen and Ivan have the same total number of coins. That is the quantity the question holds constant. Children skim past it because it has no number attached, yet it is the hinge of the whole problem. The moment you fix on it, the question stops being about masses and money in general, and becomes a question about one thing only: the swap between the two coin types.
Here is the swap. Ivan has 104 twenty-cent coins and Helen has 64, so Ivan has 104 minus 64, that is 40, more twenty-cent coins than Helen. But their totals are equal. So wherever Ivan has 40 extra twenty-cent coins, Helen must have 40 extra fifty-cent coins to keep the total the same. The two collections are identical except for this: 40 of Helen's fifty-cent coins stand where 40 of Ivan's twenty-cent coins stand. Everything else cancels.
Part (a): who has more money
Once you see that those 40 coins are the only difference between the two collections, part (a) is short. Forty fifty-cent coins are worth $20. Forty twenty-cent coins are worth $8. Every other coin is matched between the two children, so the difference in money is just $20 minus $8, that is $12. Helen, who holds the higher-value coins in that swap, has more money, by $12.
Part (b): the total mass of Ivan's coins
Part (b) uses the same swap, now read through mass. Each fifty-cent coin is 2.7 g heavier than each twenty-cent coin. So every time you replace one fifty-cent coin with one twenty-cent coin, the collection gets 2.7 g lighter. Ivan's collection is exactly Helen's with 40 such replacements, his 40 twenty-cent coins standing where her 40 fifty-cent coins stood.
So Ivan's coins are 40 times 2.7, that is 108 g, lighter than Helen's. In kilograms, 108 g is 0.108 kg. Helen's coins weigh 1.134 kg, so Ivan's weigh 1.134 minus 0.108, that is 1.026 kg.
Part (a)
Helen has more money
Part (b)
total mass of Ivan's coins
Independently solved, matches the GPA marking-scheme key. You can also read the full worked solution.
The takeaway worth keeping
The move that unlocks this question is not a coins trick. It is a habit: find the quantity the question holds constant, here the number of coins, and compare across that. The same constant carried part (a) in dollars and part (b) in grams, which is why one idea did both. This is the engine behind a whole family of before-and-after questions, where something is given away, added, transferred or swapped, and one quantity quietly stays fixed.
If your child froze on this one, it is almost never the arithmetic. It is that they started computing before they found the thing that stays the same. For more in this family, our before-and-after questions guide trains exactly that reading, and our hardest-questions hub collects the others that ask for the same move.