Let’s play darts!!

In the 501 game of darts players take turns at throwing 3 darts to reduce their score to zero.

A “checkout” refers to the process of finishing a game by reducing a player’s score to exactly zero, by hitting a double or the bullseye (50 points) with the final dart.

For example, if a player has 40 remaining, they can hit the double 20 (D20) to win.

Here is an example of a 3 dart checkout:

120 : T20 20 D20    (treble 20, single 20, double 20)

  1. The maximum checkout is 170. How can you make this?
  2. For which numbers between 140 to 170 can you find a three dart checkout?
140 150 160 
141 151 161 
142 152 162 
143 153 163 
144 154 164 
145 155 165 
146 156 166 
147 157 167 
148 158 168 
149 159 169 

Most darts players like to aim to finish on D20, D18, D16 or maybe Bullseye.

  1. A player has 94 left with three darts. They aim for T18
  2. What is their checkout if they hit T18?
  3. What is their next dart if they hit a single 18 instead?
  1. Imagine you have three darts. Would you rather a score of 32 or 30 left? Think about what happens if you just miss D16 and get single 16 left versus just missing D15 and getting single 15.
  1. What checkouts can you find for three darts on 107? What would be the best option do you think?

Extra reading

Logic behind checkouts:

Checkouts Explained

Checkout game:

Darts Math Quiz application

Hexadecimals and Binary

Why do we use base 10? How does base 16 work?

Read this brilliant article: https://betterexplained.com/articles/numbers-and-bases/.

Here is a pdf with explanations adapted from Better Explained and all the activities below. Solutions to all the activities can be found here.

Decimal1520324750170171141
HexadecimalF14202F32AAAB8D

Activity 1

Colour in all the hexagons that are multiples of 7 when converted to decimal numbers.

Activity 2

Fill in the table below. You will need to work out what the 3rd column represents in hexadecimal numbers

Decimal   1788740
Hexadecimal11BFFF1000   

Activity 3

Find the sum of 3A5 + 2D1 by converting to decimal, doing the addition and converting back to hexadecimal.


Can you do it without converting to decimal numbers?

Activity 4

What’s great about binary?

It’s the simplest number system as it only uses two digits – 1 and 0. This means it is very easy to build in hardware. You just need things that can turn on or off (representing 1 and 0), so it is fundamental to all computers. For example, in a transistor, ‘0’ means no electricity is flowing, whilst ‘1’ means there is a flow of electricity.

How are binary and hexadecimals linked?

Because one block of four binary numbers represents one hexadecimal number it is easy for programmers to visualise numbers in hexadecimal. Programmers sometimes use words written in hexadecimal in their programs.

Activity 5

What word is this?

1101 1110 1010 1101 1011 1110 1110 1111

Activity 6

From https://nrich.maths.org/problems/base-puzzle

Find the missing number

10000, ? , 100, 31, 24, 22, 20, 17, 16, 15, 14, 13, 12, 11, 10

Puzzles for Spies – from GCHQ

We looked at a lovely way to encode secret messages from a fantastic book published by GCHQ.

Here are some instructions to code using this method on excel

Challenge

A country was used as the key instead of DOLPHIN.  Given the following encodings, can you guess which country?

CHINA- 0FJBD

SCOTLAND – T0WSYDBA

KENYA – Z9BLD

BRUNEI – NGQB9J