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<p>[QUOTE=&quot;ErolGarip, post: 2815648, member: 88736&quot;]Ok, here is my coin collection, see picture. No, it is not counted as a collection? Why not, it is contemporary coin collection. Anyway, it fits this thread which is about coin and mathematics that is also in his interests of professor Dale (btw, a few of these coins are already on the way, must be already in USA now.) </p><p><br /></p><p>Now, lets back to the topic, however, lets go ahead, as an expert in mathematican and also an old engineer too may be viewing here now. </p><p><br /></p><p>Lets start the math with a simple, a classical question. We have these coins: 1kurus, 5kurus, 10kurus, 50kurus, and 100kurus=1lira. Suppose we have a lot from each of these. To make a payment total 5lira=500kurus, how many different payment options do we have? That&#039;s, suppose we have: </p><p><br /></p><p>a pcs of 1kurus, b pcs of 5kurus, c pcs of 10kurus, d pcs of 25kurus, e pcs of 50kurus and f pcs of 100kurus. Total amount will be 500kurus. </p><p><br /></p><p>Mathematical formulation is: </p><p>1a + 5b + 10c + 25d + 50e + 100f = 500 </p><p>Solve a, b, c, d, e, f. </p><p><br /></p><p>At first glance, it may seem to any person that this equation is not solvable as there is 1 equation 6 unknowns. However, when the same person runs his mind a little s/he will see it is not so, there are relations between a, b, c, d, e and f. So, actually, in this one equation, there is only one unknown and determining it will be equivalent to determining the probability in the question. However, this may not be studied in the probability field of mathematics as it is about &quot;possibility&quot; rather than &quot;probability&quot; as there is analytical certainty in this question. Anyway, proof/solution of this question may require some mathematical language such as Axiom, Lemma, Theorem, Proof, QED, etc which I myself am a foreigner to this language in their systematic. I leave this way of speaking to the mathematican. Anyway, this &quot;educational mathematics&quot; question can be left to students at elementary schools to high schools, also to university students for &quot;easiest&quot; solution. </p><p><br /></p><p>Now, suppose we do NOT have any of these available coins anywhere in the world. Let the name of currency be &quot;X&quot; instead of kurus or cent or agora or whatever. So, we will be setting up a world coin system&nbsp; from the beginning. Similar to the question above, question is: </p><p><br /></p><p>To obtain a total amount &quot;T&quot;, how many coins from each new coins are needed? </p><p><br /></p><p>Let A, E, I, O, U, etc (see only wovel letters and capitals) show their face values of new coins. </p><p>Let k, l, m, n, p, r, etc be number/pieces of each coins. </p><p>Let the dot (.) shows multiplication symbol not to confuse with x or X which is the name of coin.</p><p><br /></p><p>Now, question/problem is: </p><p><br /></p><p>k.A + l.E + m.I + n.O + p.U + .... (etc) = T(otal) .... Solve k, l, m, etc., and A, E, I, etc... </p><p><br /></p><p>See, in this one equation, everythings unknown. Is this solvable? (ok, before going into answer/talk more, first, lets wait for the coins sent to be delivered to the mathematican. For the moment, this is enough.)[/QUOTE]</p><p><br /></p>

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