DAY 12
Comment
See in what ways the tile patterns are the same.
For example, they all have 3 white tiles along the top.
What else?
And how does the number of blue tiles change with the number of
white tiles?
Answer
The pattern has 10 blue tiles.
Readers' methods
Joanne G, Weymouth DT3:
25 1 = 24.
24 / 2 = 12: 12 white tiles down one side.
12 2 = 10: there are 10 blue tiles.
Stephen G, Colchester CO3:
Number of white tiles:
subtract 1 for middle, divide by 2 because 2 sides, subtract 2
for 1 at each end.
25 1 = 24; / 2 = 12; 2 = 10 = Answer.
Jane H, Ashtead KT21:
The white squares are equal on both sides so the number of white
squares on one side is the total number minus one and then halved.
In this case 25 1 = 24, 1/2 x 24 = 12.
There are two less blue squares than white ones so the answer
is ten blue squares.
Editor's note: the above three methods
can all be illustrated by this diagram.
Michael S, Sunderland SR4:
Each pattern has 3 equal columns (2 white & 1 blue) with 3
extra white tiles on top and 2 extra white on bottom.
So 25 white tiles minus the 5 extra = 20 white.
20 white tiles = 2 columns of 10 and therefore 1 column of 10
blue.
Generally, if the number of white tiles = W, then the number of
blue tiles B = (W 5) / 2.
Noreen P, Leeds LS5:
| When there are | 2 blue tiles there are | 9 white tiles |
| 3 blue | 11 white | |
| 6 blue | 17 white. |
Lorna G, aged 16:
9 white tiles means 2 blue tiles, 11 white tiles means 3 blue
tiles, and 17 white tiles means 6 blue tiles. This gives the relationship
"add one blue, add two white", and using "w"
as white tiles and "b" as blue tiles, this gives the
formula:
w=2b+5
and with 25 white tiles:
25=2b+5
20=2b
b=10...there are 10 blue tiles.
Y7 student, Holgate NG15:
Grey tiles equals half of white tiles, after having taken 5 white
tiles away.
G = (W - 5) / 2,
so G = (25 - 5) / 2
= 20 / 2
= 10.
Y7 student, Holgate NG15:
I got my answer by following the pattern.
If there were 25 white tiles you would put 12 tiles either side,
then one in the middle, whch adds up to 25.
Then colout 10 grey tiles starting from the top and leave one
space at the bottom.