Maths quiz

Question 1A set of real numbers: 4, x, 1, 9, 6 has the property that the median of the set of numbers is equal to the mean.

What values can x be?

Question 2My digital watch uses ‘12 hour clock’ and shows hours and minutes only.

For what fraction of a complete day is at least one "1" showing on the display?

Question 3How many rectangles (including squares) can be drawn using the squares on a 4x4 chessboard?

Rotations and translations are permitted.

Question 4This network has nine edges which meet at six nodes.

The numbers 1,2,3,4,5,6 are placed at the nodes, with a different number at each node.

Question 4 (cont)Is it possible to do this so that the sum of the two numbers at the ends of an edge is different for each edge?

Either show a way of doing this, or prove that it is impossible.

This problem taken from http://nrich.maths.org/weekly

Question 5A six digit positive integer has the property that when its digits are rearranged, the new number is double the original.

What is the smallest number this can be?

Question 62013 can be written as the sum of consecutive positive integers, all of which have two digits. What are the first and last two digit numbers in the sum?

Question 7Temperature can be measured in degrees Fahrenheit or Celsius.

What temperature is represented by

the same number on both scales?

Question 82/3 of men answering this question got it right and 3/4 of women answering it got it right. The same number of men and women were correct.

What fraction of all respondents were correct?

Question 916 is a special number because when it is written as numbers with indices it can be written as either 24 or 42.

What is the next number that can be written as both xy and yx?

(where x and y are both positive integers)

=

Question 10

1 0 1 1 1 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 1 1 0 0 1 1 1 10 0 0 0 1 1 0 1 0 11 0 1 0 0 1 1 0 0 1 1 0 0 1 0

0 1 1 1 10 0 1 0 0 1 0 1 0 1 0 0 0 0 10 1 1 1 1 0 1 1 1 0

0 0 0 0 1 0 0 1 0 01 1 0 0 1 0 0 1 0 00 1 1 1 1 0 0 1 0 0 0 1 1 1 01 0 1 0 1 0 1 0 0 1

0 1 1 1 00 0 1 1 1 0 0 1 0 10 0 1 0 11 0 1 0 0

Question 11London has longitude 0°.

Cardiff has longitude 3° W.

They have the same latitude.

If the sun rose at 4:40am this morning in London, at what time did it rise in Cardiff?

Question 12In the game fizz-buzz, the positive integers are called out in order starting from 1 but replacing any number which is a multiple of 3 with ‘fizz’ and replacing any number which is a multiple of 5 with ‘buzz’.

So the game begins:

1, 2, fizz, 4, buzz, fizz, 7, 8, fizz, buzz, 11, fizz, 13, 14, fizzbuzz, 16, 17…

What is the 2013th number to be said aloud?

Question 13Joining adjacent midpoints of the edges of a regular tetrahedron creates a regular octahedron. What is the ratio of the volume of the octahedron to the volume of the original tetrahedron?

Question 14A regular octagon has side length 2.

What is its area?

(Leave answer in surd form)

Question 152013! ends in a string of zeros. How many of them are there?

Teacher notes• These questions formed the QR maths quiz at the MEI conference

2013.

• They are in approximate order of difficulty … although difficulty is in the mind of the solver!

• You might want to use a selection of these questions as a quiz for your own students. Most questions are accessible to KS4 students and younger.

• Question 9 has an alternative ‘visual’ version, please see the attached Excel sheet.

• Answers on the next page

Answers

1. 0, 5, 10

2. ½

3. 100

4. Impossible. Sum of edges has to be 63 (sum of 3 to 11) whereas each node is even, hence each of the 1-6 digits will be used 2 or 4 times each. This will give an even total.

5. 142 857 and 285714

6. 45 and 77

7. -40

8. 12/17

9. No other positive integer solutions exist

10. 13

11. 4:52am

12. 3773

13. ½

14. 8+8√2

15. 501