All Questions
3
questions
19
votes
1
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Can we partition the reciprocals of $\mathbb{N}$ so that each sum equals 1
Let $S = \{1, 1/2,1/3,\dots\}$
Can we find a partition $P$ of $S$ so that each part sums to 1, e.g.
$$P_1 = {1}$$
$$P_2 = { 1/2,1/5,1/7,1/10,1/14,1/70}$$
$$P_3 = {1/3,1/4,1/6,1/9,1/12,1/18}$$
$$P_4 = \...
- 702
2
votes
1
answer
60
views
Can a number be partitioned into parts satisfying this condition? [closed]
Let $a,b,c,d,e,f$ be distinct decimal digits, with $ab,cd,ef$ being two-digit numbers formed from these digits (so that, for example, $ab=10a+b$).
How may I prove that the expression $ab+cd+ef$ ...
- 33
2
votes
1
answer
289
views
Using natural numbers $1,2,...n,$ in how many ways can the number $n$ be formed from the sum of **one** or more smaller natural numbers?
Using natural numbers $1,2,...n,$ in how many ways can the number $n$ be formed from the sum of one or more smaller natural numbers?
I thought it would be an easy problem but i couldn't figure it out....
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