MATHS WEEK is under way and, as is our annual tradition, we’re setting our readers some puzzles every night. Give them a go! You can check out other events being held over the week here. 

Today is Ada Lovelace Day

Ada Lovelace (1815-1852) lived at a time when there were great barriers in education for women. However, Ada was from an aristocratic family and her mother ensured she was educated at home by private tutors and this included maths and science.

Ada excelled at maths and became friendly with Charles Babbage, one of the top mathematicians of the age.

Babbage invented a mechanical computer which he called the Analytical Engine (which was never built) and Ada is credited with writing the first computer program for it. She is commemorated on Ada Lovelace Day, which will be celebrated today.

Here are some puzzles that involve computational thinking, but don’t require any programming knowledge.

1) A computer can only compare two adjacent numbers and swap them if the number on the left is larger.

What is the minimum number of steps to sort the following list of numbers into ascending order?

7, 2, 9, 1, 5

2) Binary code represents any number as a combination of 1s and 0s which makes it ideal for computers to process (electrical signal on = 1 off = 0).

Using 4 digits one can count to 0-15. Here is 0-7:

0 = 0000 

1 = 0001 

2 = 0010

3 = 0011

4 = 0100

5 = 0101

6 = 0110

7 = 0111

a) Convert the following string to decimal numbers?

0010 0000 0010 0110

b) What is 14 in binary?

c) If 1=A and 2=B and so on, what does the following binary string spell out?

0001 0100 0001

d) If 1=A and 2=B and so on, what does the following binary string spell out?

0001 1110 0111 1100 0101

3) You have five cards with the values 1, 2, 4, 8 and 16.

a. Can you make all the numbers between 1 and 31 using combinations of these cards? (You don’t have to use them all for each number.)

b. Can you make every whole number from 0 to 31 by adding the values of the face-up cards?

4) You have a very simple computer that can only run two commands.

Command A: Multiply the number displayed by 2.

Command B: Add 1 to the number displayed.

The machine starts at 0.

What is the fewest number of commands needed to reach 100?

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Monday’s puzzle: The answers 

1. You break even (€0)

2. 20% profit

3. €64

4. €90

5. First Bureau (£249.24 versus £243.90)

6. You make a €10 loss overall