Digits and numbers are wonderful toys. The number of problems with them surpasses the imagination. Still, great minds think alike.
In 2013 I posed a classical problem to make as many numbers as possible by combining four fours.
In March I posed the challenge to make all the numbers of 0 to 20 by combining 5 5’s.
1) 6 6’s***/*****
Today’s problem is a sequel: make all the numbers 0 till 20 using 6 6’s. You can use brackets, +,-,*,/, ^and sqrt. You msy use ! for just one of the numbers.
You can check your solutions here and here
When googling, I found the puzzle masters at occupymath have posed the same challenge.
3) general ***/*****
The next problem is not, as you may have thought, to make all numbers 0-20 with 8 8’s. Rather the question is, can the numbers 0-20 with made with all digits? In base 11, in base 12?
For a start:
0 = (n-n)*(n+…+n)
1 = n/n + (n-n)*(n+…+n)
2 = n/n + n/n + (n-n)*(n+ … + n)
and so on.