#248 Pizza parity
Set by Mary Ellis
鈥淵ou know how you ordered one medium pepperoni pizza and one medium broccoli pizza?鈥� said the delivery man. 鈥淲ell, unfortunately the order got a bit mixed up and I have one large pepperoni pizza and one small broccoli pizza.鈥�
鈥淣o big deal!鈥� exclaimed Poppy. 鈥淭here鈥檚 two of us, so we鈥檒l each take half of both pizzas and we鈥檒l have the same amount!鈥�
鈥淕ood plan,鈥� said Toby, 鈥渆xcept for the part where I have to take any amount of your broccoli pizza 鈥� you know that I hate broccoli! Now, if I can just work out the ratio between a large and small pizza, then use the area of a circle to鈥︹��
Poppy smiled and grabbed a pizza cutter. Without slicing the small pizza at all, she made a single cut that allowed them to each take half of the total amount of pizza, while giving Toby only pepperoni.
How did she manage it?
Solution next week
#247 Bargain birthday badges
Solution
Grandad only needs to buy 12 badges to cover 21 birthdays.
He will need a badge for 1 as well as one for each of the prime numbers up to 21. That is 2, 3, 5, 7, 11, 13, 17 and 19. He will then need extra badges for composite (non-prime) numbers that have repeated prime factors. For example, 4 is 2 脳 2, so he will need either an extra 2 or a 4. By choosing a 4, he won鈥檛 need an 8. Continuing to build his badge collection in this way gives Grandad one possible final set: 1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19.
Quick quiz #228
set by Bethan Ackerley
1 Fresnel and Fraunhofner are two types of what?
2 Which Earth year is commonly adopted as the beginning of the Martian calendar, as proposed by researchers in 2000?
3 Which French neurologist is mentioned in the novel Dracula?
4 In which city is the main Nobel prize ceremony held?
5 Jiahu in China is a site associated with which Neolithic culture?
Quick quiz #228
Answers
1 Diffraction
2 1955
3 Jean-Martin Charcot
4 Stockholm
5 The Peiligang culture