Today’s problem — free all day, every step. Every day has one.
Pebbles — Ali and Ben end up equal
Ali and Ben had a total of 100 pebbles. Ali gave of his pebbles to Ben. Ben then gave of his pebbles to Ali. In the end, each of them had the same number of pebbles. How many pebbles did each of them have at first?
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The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Pebbles only move between the two boys, so the total is pinned at 100 the whole way — that fixes the end state at 50 each, and from a known end you can undo the transfers in reverse order.
How to spot it
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Common mistake
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
Try one like it
Challenging Marbles — Priya and Zara swap shares Priya and Zara had a total of 160 marbles. Priya gave 1/3 of her marbles to Zara. Zara then gave 1/5 of her marbles to Priya. In t…The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.