One way of making sure all possibilities were included came from

**Emma** and
**Abi** of Moorfield Junior
School found the following combinations of three biscuits from the
$12$ different varieties, this was the same as that sent in by
**Sarah and Helen** from
Glenmead Primary in Birmingham. They show their answers as
**a list**, but first they
explain the strategy they used to help them with so many
possibilities:

First, we started with alphabetically, ABC, DEF, GHI and
JKL.

Then we did the first letter of the first three biscuits
(ADJ).

Next we took the second letters (BEH) of each plate of
biscuits.

Finally, we sorted out the ones left over.

The possible plates of biscuit varieties that the girls came up with were:

HIG | HKJ | ABC | DEF |

ADJ | EBH | AIK | FIC |

KLA | DBG | LEC | FLG |

**Prateeksha** , from
Riccarton Primary School, shows a slightly different strategy. It
is **a list** like Emma and
Abi's but can you see how the information has been organised in
this list? The organisation is what shows Prateeksha's
thinking.

Plate A contains biscuits A, H, L |

Plate B contains biscuits B, H, K |

Plate C contains biscuits C, B, A |

Plate D contains biscuits D, A, J |

Plate E contains biscuits E, B, D |

Plate F contains biscuits F, E, C |

Plate G contains biscuits G, J, K |

Plate H contains biscuits H, G, E |

Plate I contains biscuits I, D, C |

Plate J contains biscuits J, L, I |

Plate K contains biscuits K, I, F |

Plate L contains biscuits L, G, F |

Is this list the same as **Terry** and **Daren's** from Alma Primary School in
London?

plate 1. AKL |

plate 2. BDK |

plate 3. FIJ |

plate 4. DGI |

plate 5. BEH |

plate 6. FGL |

plate 7. BGJ |

plate 8. AHI |

plate 9. CEJ |

plate 10. ACF |

plate 11. CHK |

plate 12. DEL |

**Helen** and
**Joanna** from W.C.P.School
in Manchester sent in **a
list** of their 'plates' and used letters to represent the
biscuit varieties, as did **James** from Girton Glebe Primary School
near Cambridge. Although the order of their answers was different,
the combinations were the same.

**Hannah, Amy, Jenny**
and **Emma** , also from
Moorfields School, seem to have a completely different way of
figuring out their solution. But have they?

Can you see what they have done?

- Almond fingers on plates 1,2,3
- Bourbon on plates 4, 5, 9
- Chocolate chip on plates 7, 8, 9
- Digestive on plates 5, 6,10
- Easter biscuits on plates 4, 8,12
- Fig rolls on plates 2, 4, 7
- Ginger-nuts on plates 3, 9, 11
- Honey cookies on plates 2,10,11
- Iced Wafers on plates 1, 5, 8
- Jammy Dodgers on plates 3, 6, 10
- Kiwi cookies on plates 1, 7,6
- Lemon puffs on plates 6,11,12

But how do you keep track of all that information? This is what
**Alex** from Brecknock
School did:

I started with abc, then def, ghi, jkl and then mixed them
up.

I made a list of all the biscuits as they were used, after that I
crossed out a letter every time I used one of that type.

a | d | g | j | l | c | l | f | b | j | k | b |

b | e | h | k | h | e | h | i | k | c | a | f |

c | f | i | l | d | g | a | j | i | d | e | g |

Hmm, it looks like 'a and f' in the centre line are not matched with other biscuits. Why do you think that is?

**Oskar** , a fellow
pupil from Brecknock Primary, started with A(lmond finger) and I
moved 1 A forward 1 place and another A forward 2 places. I did the
same with the next plate then the next plate and so on. The
solution ended up like this:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

k | l | a | b | c | d | e | f | g | h | i | j |

l | a | b | c | d | e | f | g | h | i | j | k |

a | b | d | e | f | g | h | i | j | k | l |

**Nathan** , also from
Brecknock explains; first I wrote **a table** .

I started with kbc then I made sure that I used each biscuit
once

I continued with the rest of the biscuits. When I had used all the
biscuits I had to mix the biscuits about. This was my answer:

kbc, def, ahf, jk, dbe, bgc, jhb, fki, aij, iel, lgd, gca.

The students of **Ms Brown's
class** also organized their information in **a table** , but in different way then
Oskar. Did they arrive at a different answer the other pupils
above?

They begin by explaining their notation. They used a combination of letters (for the variety of biscuit) and numbers (to show if it was the first, second or third biscuit selected).

Notation:

**A** lmond Fingers = A1 (biscuit 1), A2 (biscuit 2),
A3 (Biscuit 3).

**B** ourbon = B1, B2, B3.

**C** hocolate Chip = C1, C2, C3.

**D** igestive = D1, D2, D3.

**E** aster Biscuits = E1, E2, E3.

**F** ig Rolls = F1, F2, F3.

**G** ingernuts = G1, G2, G3.

**H** oneynut cookies = H1, H2, H3.

**I** ced Wafers = I1, I2, I3.

**J** ammy Dodgers = J1, J2, J3.

**K** iwi Cookies = K1, K2, K3.

**L** emon puffs = L1, L2, L3.

Working it out:

Altogether there are $36$ Biscuits.

$12$ types of biscuits and $12$ plates.

So, what did they do with the information? They used a spreadsheet and built a table like this. One of the pupils explains:

Put A-B-C together, D-E-F together, G-H-I together and J-K-L together:

Now there are $2$ of each biscuit left.