Question 17
Peter Pan takes the three siblings Wendy, John and Michael to Neverland. There are flowers with different numbers of petals: four, six, and so on. Strangely, the orange petals and yellow centre are all circles. Each circle contains a secret number, and every straight line through two petals and the centre has the same total. The pictured four-petal flower is an example: each line totals 8, since 2 + 1 + 5 = 8 and 3 + 1 + 4 = 8.
The numbers appear only when Peter touches them, so the siblings do not yet know the secret numbers. Peter promises to teach them to fly if they can find the numbers at the flower centres. They eagerly answer his hints.
1. Peter points to a four-petal flower that will contain 1, 2, 3, 4 and 8. Wendy answers these questions:
– Which pairs among these numbers have equal sums?
– Which number is absent from those pairs? Hence, which number can be in the centre?
2. Michael and John choose a six-petal flower containing 1, 2, 3, 4, 5, 6 and 7. Which numbers can be at its centre?
The numbers appear only when Peter touches them, so the siblings do not yet know the secret numbers. Peter promises to teach them to fly if they can find the numbers at the flower centres. They eagerly answer his hints.
1. Peter points to a four-petal flower that will contain 1, 2, 3, 4 and 8. Wendy answers these questions:
– Which pairs among these numbers have equal sums?
– Which number is absent from those pairs? Hence, which number can be in the centre?
2. Michael and John choose a six-petal flower containing 1, 2, 3, 4, 5, 6 and 7. Which numbers can be at its centre?