# Sample Task Kit for Home Lending

order, or use Control F to search.
• Back to Back Building

• Crazy Animals
There are 27 animals altogether. Any one of 3 heads can go with anyone of 3 middles, which can go with any one of 3 legs. So, 3 x 3 x 3 = 27.
Therefore in the extension there would be 64 animals made from 4 x 4 x 4.
Kangaroo could be split as k-anga-roo or kang-a-roo.

• Crossing The Desert
Two possibilities are shown and there could be minor variations to these.
• On Day 4, one traveller gives 1 day's rations to the other, buries 4 day's rations, and returns home. The other traveller retrieves the buried rations on the return journey from the oasis.
• On Day 3, one traveller gives 3 day's rations to the other, buries 4 day's rations and returns home. The other traveller retrieves the buried rations on the return journey from the oasis. This solution has 2 day's rations to spare.

• Cube Nets
You could organise your search to look for nets with the longest chain of squares being 4-in-a-row, 3-in-a-row, 2-in-a-row.
A mathematician would check every possibility. What do you think would be the result of including 6-in-a-row, 5-in-a-row, 1-in-a-row?

• Farmyard Race Day
There are three forms of this task depending on the availability of animals. The different forms are numbered 125, 125A, 125B.
1.
 Task No. 125 125A 125B Winner... Sheep Goat Chicken 3 lengths behind... Duck Duck Duck 7 lengths behind... Cow Cow Cow 8 lengths behind... Pig Pig Pig 10 lengths behind... Horse Horse Horse
2.
The unnecessary clue is: The pig did not finish last. (125, 125A, 125B)
3.
 Task No. 125 125A 125B Winner... Pig Pig Pig 1 lengths behind... Sheep Goat Chicken 4 lengths behind... Duck Duck Duck 6 lengths behind... Cow Cow Cow 9 lengths behind... Horse Horse Horse
4.
The dog watched 5 lengths behind the winner, in the length between the duck and the cow. (125 & 125A)

The rabbit watched 5 lengths behind the winner, in the length between the duck and the cow. (125B)

• Highest Number 1

• Ice-Cream Flavours
Assuming no repeats of flavours are allowed:
• If a fourth colour and triple headers are used, there are 24 different ice-creams.
• If a fourth colour and quadruple headers are used, there are also 24 different ice-creams!
• If a fifth colour and triple headers are used there, there are 60 ice-creams.

• McMahon's Triangles 2
• 4 small hexagons

• 1 large hexagon using 24 pieces

• Mirror Patterns 1
Here are solutions to some of the harder challenges.

Puzzle H

Puzzle I

Puzzle K

Puzzle N

• Number Tiles

 295 +173 468 658 +314 972 187 +452 639 659 +214 873 736 +245 981

• There are 42 different combinations that add to 18.

• Photo Angles
• Camera
From the front right hand corner of the grid, the camera position was 12cm to the right, 50cm towards the front and 30cm vertically.
• Light
From the front left corner of the grid, the light was 75cm to the left, 15cm towards the front and 50cm vertically.

• Pick A Box
39 = 1 + 4 + 7 + 12 + 15
40 = 3 + 5 + 8 + 10 + 14
41 = 2 + 6 + 9 + 11 + 13

• Planets
The cards are placed in the sequence shown in the picture at the distances shown. (A little extra string is provided at each end.)

• Police Line Up
The answer is BERT. However, there arguably could be two answers according to how you interpret the clue:
Frankie is standing between Bugsy and Clyde.
If this is taken to mean somewhere between, then the answer could be CLYDE or BERT.

• Racetrack

• Thirty One
A winning strategy is to be first to the numbers 24, 17, 10 or 3.
• If you are on 3 you can always get to 10 no matter what your opponent plays.
• Similarly, if you are on 10 you can always get to 17, then 24, then 31 and win.
An exception occurs when you get to say 27 and need a 4, but there are no 4s left. Then the game is a draw. If you are playing the winning strategy above, how should your opponent play to force this draw?

• Truth Tiles
One solution is:
4 + 5 = 9
8 - 1 = 7
3 x 2 = 6

However, there are four solutions which can be developed from 3 x 2 = 6.

 4 + 5 = 9 8 - 1 = 7 3 x 2 = 6 4 + 5 = 9 8 - 7 = 1 3 x 2 = 6 7 + 1 = 8 9 - 4 = 5 3 x 2 = 6 7 + 1 = 8 9 - 5 = 4 3 x 2 = 6
These answers assume 4 + 5 = 9 and 5 + 4 = 9 are not different and that 3 x 2 = 6 is not different to 2 x 3 = 6.

• Who Lives Where?

 NUMBER 1 NUMBER 3 NUMBER 5 Papadopoulos Nguyen Jackson Sam Kim Chris Ford Falcon Holden Commodore Mazda 323

• Who Owns The Monkey?