Each of a collection of 144 tiles is either triangular or square, either red or blue, and either wooden or plastic. Given that there are 68 wooden tiles, 69 red tiles, 75 triangular tiles, 36 red wooden tiles, 40 triangular wooden tiles, 38 red triangular tiles, and 23 red wooden triangular tiles, how many blue plastic square tiles are there?

23

Step-by-step explanation:

We have to fill in the following tree (upside down)

TRW=? TRP=? TBW=? TBP=? SRW=? SRP=? SBW=? SBP=?

TR=? TB=? SR=? SB=?

T=? S=?

Where TRW means TriangularRedWooden, SBP SquareBluePlastic and so on.

We are going to fill in the entrances (?) from bottom to top by using the data provided.

75 triangular tiles T=75, S=69 (there are 144 tiles)

TRW=? TRP=? TBW=? TBP=? SRW=? SRP=? SBW=? SBP=?

TR=? TB=? SR=? SB=?

T=75 S=69

38 red triangular tiles. TR=38 TB=37 (75-38)

TRW=? TRP=? TBW=? TBP=? SRW=? SRP=? SBW=? SBP=?

TR=38 TB=37 SR=? SB=?

T=75 S=69

69 red tiles. SR=31 (69-38) SB=38 (69-31)

TRW=? TRP=? TBW=? TBP=? SRW=? SRP=? SBW=? SBP=?

TR=38 TB=37 SR=31 SB=38

T=75 S=69

23 red wooden triangular tiles. TRW=23 TRP=15 (38-23)

TRW=23 TRP=15 TBW=? TBP=? SRW=? SRP=? SBW=? SBP=?

TR=38 TB=37 SR=31 SB=38

T=75 S=69

36 red wooden tiles. SRW=13 (36-23) SRP=18 (31-13)

TRW=23 TRP=15TBW=? TBP=? SRW=13 SRP=18 SBW=? SBP=?

TR=38 TB=37 SR=31 SB=37

T=75 S=69

40 triangular wooden tiles. TBW=17 (40-23) TBP=20 (37-17)

TRW=23 TRP=15 TBW=17 TBP=20 SRW=13 SRP=18 SBW=? SBP=?

TR=38 TB=37 SR=31 SB=38

T=75 S=69

68 wooden tiles. SBW=15 (68-23-17-13) SBP=23 (38-15)

TRW=23 TRP=15 TBW=17 TBP=20 SRW=13 SRP=18 SBW=15 SBP=23

TR=38 TB=37 SR=31 SB=37

T=75 S=69

Our tree is filled up!

how many blue plastic square tiles are there?

SquareBluePlastic = SBP = 23