Question P5–P6 Constant total
Today’s problem — free all day, every step. Every day has one.
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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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.
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
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.
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