I have six tiles numbered 1 to 6. Each is a different shape, (triangle, circle, square, pentagon, hexagon and octagon) and painted a different color (red, orange, blue, yellow, green and purple.)
I arranged the tiles in two rows of 3. Given that

1) The top row formed an odd number and the bottom row a prime number
2) In the bottom row the colors were in reverse alphabetical order.
3) The Blue Number 1 was between the orange tile and the Circle;
4) The Hexagon was directly above the Red triangle numbered 4.
5) One tile has a color and shape beginning with the same letter.

Can you reproduce the layout?

(In reply to Apology - Correction by Vernon Lewis)

Actually there are 12 solutons to the problem as listed:

215   215   215   215   215   215   215   215   215   215   215   215
oby   oby   gbo   gbo   gbo   obg   obg   obg   obp   obp   pbo   pbo
hoc   hsc   cho   cho   chs   ohc   ohc   shc   ohc   ohc   cho   cho

463   463   643   643   643   643   643   643   643   643   643   643
rpg   rpg   yrp   yrp   yrp   yrp   yrp   yrp   yrg   yrg   yrg   yrg
tps   tpo   pts   stp   otp   pts   stp   otp   pts   stp   pts   stp

where the colors are listed directly under the digits and the shapes directly under the colors.

Only one of these satisfies a condition that was originally in the puzzle in the queue: that the bottom row shapes also be in reverse alphabetic order.

   50   cls
 1000   S="sphoct":N="123456":C="ygprbo"
 1010   Nh=N
 1020   repeat
 1030    Topnum=val(left(N,3)):Botnum=val(right(N,3))
 1040    if Topnum@2=1 and prmdiv(Botnum)=Botnum then
 1050     :Ch=C
 1060     :repeat
 1070       :Ix1=instr(N,"1"):Ix2=instr(C,"o"):Ix3=instr(C,"b")
 1080       :if Ix1=Ix3 and (Ix1=2 or Ix1=5) and abs(Ix2-Ix1)=1 then
 1090         :if mid(C,4,1)>mid(C,5,1) and mid(C,5,1)>mid(C,6,1) then
 1100          :Sh=S
 1110          :repeat
 1120           :Circ=instr(S,"c")
 1130           :Hexagon=instr(S,"h")
 1140           :if abs(Ix1-Circ)=1 and Circ<>Ix2 then
 1160             :Red=instr(C,"r"):Triangle=instr(S,"t"):IxFour=instr(N,"4")
 1170             :if Red=Triangle and Red-Hexagon=3 and IxFour=Triangle then
 1171              :Good=0
 1172              :for Tile=1 to 6
 1173               :if mid(C,Tile,1)=mid(S,Tile,1) then Good=1:endif
 1174              :next
 1178              :if Good then
 1179               :Row=(Ct\12)*10+1:Col=(Ct@12)*6+1:Ct=Ct+1
 1180               :locate Col,Row:print left(N,3):locate Col,Row+1:print left(
C,3):locate Col,Row+2:print left(S,3)
 1181               :locate Col,Row+4:print right(N,3):locate Col,Row+5:print ri
ght(C,3):locate Col,Row+6:print right(S,3)
 1182              :endif
 1190             :endif
 1210           :endif
 1220           :gosub *Permute(&S)
 1230          :until Sh=S
 1240         :endif
 1250       :endif
 1260       :gosub *Permute(&C)
 1270     :until Ch=C
 1280    :endif
 1290    gosub *Permute(&N)
 1300   until Nh=N
 9999   end

Note that the at-sign is part of the UBASIC programming language representing MOD. The comment editor automatically makes these e-mail address links, which they are not.

The Permute subroutine is elsewhere on the site.

Posted by Charlie on 2007-02-25 14:21:04