OK, curiosity got the better of me and I looked up the TWIDO insturction set.
http://www.telemecanique.com/85256E69002E481A/all/CC1EC5F7B51A94ABC1256F4D004A53F3/$File/31003914k01002.pdf
As it is a Telemecanique product I wondered if its ladder might be similer to Modicon 984 Ladder, and it is similar.
Like the Modicon 984, the Twido uses a 7x11 array solver that solves the 1st column top to bottom, then the second colum top to bottom, etc. We can take advantage of that solve order to build a simple flip flop, which while it should work in the Twido, won't work in other PLCs (such as AB) that use stack solvers instead of array solvers.
%I.0.0.0 %M1 %M1
----]P[---+----]\[--------(S)
|
| %M1 %M1
+----] [--------(R)-
-]P[- is a rising pulse input instruction. It will be true for only one scan when the button is first pressed. If %M1 is off then it will be set. If it is on then it will be reset. Because the rung is solved in vertical columns there is no chance that the -(R)- will overwrite the -(S)-. Thus, bit %M1 will turn on and stay on when the button is pushed once and turn off when the button is pushed a second time. You can also use a -(R)- coil off the timer to also reset the %M1 bit when the timer is done.
I don't want to give you a complete solution for your homework, but I'm willing to start you in the right direction. I hope this helped.
disclaimer: I have never programmed a Twido but I am basing this upon what I know about similar PLCs and I had a look at the programming manual.