Each boy appears in exactly two of the three pairs. So adding all three pair-totals counts every boy twice.

Paul+Simon25Simon+Gray18Paul+Gray172 × total = 60

Plain numbers are given; italic underlined numbers are worked out.

  1. Add all pairs → 25 + 18 + 17 = 60
  2. This counts each boy twice → 2 × total = 60
  3. Total → 60 ÷ 2 = 30

The three boys have 30 cards in total.

Check: Paul 12, Simon 13, Gray 5 → 12+13=25, 13+5=18, 12+5=17; total 30. ✓