Write your answer on the answer sheet provided by your teacher. Year 8 Milton Keynes Mathematics Challenge in partnership with Bletchley Park 2018

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Rolf McKinney
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1 Write your answer on the answer sheet provided by your teacher. Don t forget to write in your name and class. All pupils taking part will be awarded a Milton Keynes Mathematics Challenge pencil. If you do well you may be chosen to represent your school in the final round for all secondary schools in Milton Keynes. Year 8 Milton Keynes Mathematics Challenge in partnership with Bletchley Park 2018 First Round: Secret Mission solve the problems to save the country HAVE FUN Have fun with these puzzles. We will be pleasantly surprised if you can answer them all, but try your best. Write your answers on the separate answer sheet.

1. Count the Rectangles 10. Operation Pied Piper How many rectangles are there altogether in the M109A6 Paladin tank? A salesman knocks on the door of a house.

2 1. Count the Rectangles 10. Operation Pied Piper How many rectangles are there altogether in the M109A6 Paladin tank? A salesman knocks on the door of a house. When A a government lady answers, official he asks, knocks How on many house children number do 9. you A lady have? answers the door, the official asks, How She many replies children Three. do When you have? he asks She What replies are Three. their ages? He then She asks decides What not are to their answer. ages? He apologises refuses and asks to answer for a hint how about old they the are so in- She stead children's the official ages. She asks says for a If clue. you She multiply says their If you three multiply ages their you get three 36 (their ages you ages get are 36 exact (their ages numbers). are exact numbers). He He thinks thinks for for a a while while and and then then asks asks for for another hint. hint. The sum of of their ages is is the number on on the house house next next door. She This closes is still the not door enough and information, leaves the government so he asks official for one to last answer hint. his own question. How All old right are the the eldest children? plays the piano! He then knows their ages. Total =

3 9. Powerful Maths O, E, C, S, D each represent one of the digits 2, 3, 5, 6, 9 If O C - D + E S = CODES Find which letter represents which number. 2. Cubes Here are two drawings of the same cube from different angles. These cubes are used as a key to open a secret room at Bletchley Park, all you need is the net of the cube. o O E C S D Draw in the symbols on the net below so that it can be folded into the cube above.

4 3. Disarm the bomb 8. Huts at Bletchley Park The Codebreakers at Bletchley worked in numbered huts. During the planning stages, the huts were numbered. Can you complete the hut numbers below using all the integers from 1 to 16 so that the total of each column and of each row is exactly 34? A bomb has been found in central Milton Keynes, In order there to open are up some a lock instructions. to get into The a instructions top secret room say; Only in Bletchley a sum of Park a you thousand have to arrange will disarm eight this 8 s.so bomb, that you when can only they use are the added number up they 8 eight will times total 1,000. eg = 1864 Can you disarm the bomb? Hint: Can eg you crack the = 1864 code?

5 7. Relations 4. Marching Formations A couple is to be selected for a covert mission behind enemy lines in France. They will act as newlyweds settling in a village, where they will become part of the community. They can then spy on German army activities. The mission will last several years, so the couple need to be as young as possible. John s wife is Tom s elder sister, Mary and her elder brother Nick is married to Tom s wife s younger sister, Jane. Tom s brother-in -law is Kate s elder brother. If the ages of the six married people above all lie within two years of each other, which couple has the lowest sum of their ages? Tom John Nick Jane Mary Kate 35 pencils soldiers are arranged in in the spiral pattern shown as here. Move shown four above. of Move the pencils four of to the new soldiers positions to so new that positions three so prefect that they squares make are three formed. perfect square formations. Answer and

6 5. Add a line 6. The Bletchley Park Dance There has been a typing error in the sum below, can you work out where the typewriter has missed out a line to make the sum correct? = 550 The American Soldiers stationed at Bletchley Park loved their dances. The live band were playing jazz, and there were 15 people at the dance. By the end of the evening every person had been formally introduced and shaken hands with everyone else. How many hand shakes took place?

Grade 7/8 Math Circles. Mathematical Puzzles

Grade 7/8 Math Circles. Mathematical Puzzles Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Mathematical Reasoning Grade 7/8 Math Circles October 4 th /5 th Mathematical Puzzles To many people,