One strategy for ranges that are powers of 2 is to split the range in half and flip a coin. If it's heads, the upper half is your new range. If it's tails, the lower half is your new range. Repeat until you have a single number. This gives you a truly random number.
Another strategy comes from George Marsaglia, on this Google Groups page: https://groups.google.com/forum/m/?hl=en#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ
Choose a 2-digit number, say 23, your "seed".
Form a new 2-digit number:
the 10's digit plus 6 times the units digit.
The example sequence is
23 --> 20 --> 02 --> 12 --> 13 --> 19 --> 55 --> 35 --> ...
and its period is the order of the multiplier, 6, in the group of residues relatively prime to the modulus, 10. (59 in this case).
The "random digits" are the units digits of the 2-digit numbers, ie, 3,0,2,2,3,9,5,... the sequence mod 10.
The arithmetic is simple enough to carry out in your head.
I don't know what the distribution is, but the numbers look random, at least to me. You could also concatenate digits to create larger numbers. You could then get a pseudo-random number for any specified length of number (i.e. 2 digits, 3 digits, etc).
A similar question with many potential answers in the comments can be found at https://philosophy.stackexchange.com/questions/1961/are-people-capable-of-generating-a-random-number.