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On the same floor (Posted on 2016-11-22) Difficulty: 3 of 5
How many solutions (m,n positive integers only) are there for
floor(m/6)=floor(n/13) ?

List them.

No Solution Yet Submitted by Ady TZIDON    
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Solution re(2): How many...... g o o f | Comment 8 of 13 |
(In reply to re: How many...... g o o f by Ady TZIDON)

I. In the original problem, even if m and n are limited to positive integers there are still aleph-null solutions as there are the same transfinite cardinality of natural numbers (positive integers)  as there are integers.

II. Modified problem:

m=1 thru 5: lhs = 0; 5 values of m, 12 values of n: 60 combos

m=6 thru 41; lhs = 1 thru 6; 36 values of m, but
n=13 thru 38; rhs = 1 thru 2; 26 values of n for 6*13=78 combos
and n= 39 thru 50; rhs=3; 12 values of n for 6*12 = 72 combos

Total: 60+78+72 = 210 combinations of m and n, the highest m actually being 23, where both sides are 3.

  Posted by Charlie on 2016-11-22 22:17:10
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