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Given-is-a-square-with-side-length-15-We-need-to-find-exactly-17-smaller-squares-to-fill-the-big-one-How-many-solutions-are-possible-Note-it-s-not-enough-to-find-squares-with-the-sum-of-their-are




Question Number 206806 by Frix last updated on 26/Apr/24
Given is a square with side length 15.  We need to find exactly 17 smaller squares  to fill the big one. How many solutions are  possible?  (Note: it′s not enough to find squares with  the sum of their areas being 225, they must  fit into the 15×15 square. Example with  3 squares: 2×2+5×5+14×14=225 but  you cannot fit these in a 15×15 square)
$$\mathrm{Given}\:\mathrm{is}\:\mathrm{a}\:\mathrm{square}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length}\:\mathrm{15}. \\ $$$$\mathrm{We}\:\mathrm{need}\:\mathrm{to}\:\mathrm{find}\:\mathrm{exactly}\:\mathrm{17}\:\mathrm{smaller}\:\mathrm{squares} \\ $$$$\mathrm{to}\:\mathrm{fill}\:\mathrm{the}\:\mathrm{big}\:\mathrm{one}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{are} \\ $$$$\mathrm{possible}? \\ $$$$\left(\mathrm{Note}:\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{find}\:\mathrm{squares}\:\mathrm{with}\right. \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{areas}\:\mathrm{being}\:\mathrm{225},\:\mathrm{they}\:\mathrm{must} \\ $$$$\mathrm{fit}\:\mathrm{into}\:\mathrm{the}\:\mathrm{15}×\mathrm{15}\:\mathrm{square}.\:\mathrm{Example}\:\mathrm{with} \\ $$$$\mathrm{3}\:\mathrm{squares}:\:\mathrm{2}×\mathrm{2}+\mathrm{5}×\mathrm{5}+\mathrm{14}×\mathrm{14}=\mathrm{225}\:\mathrm{but} \\ $$$$\left.\mathrm{you}\:\mathrm{cannot}\:\mathrm{fit}\:\mathrm{these}\:\mathrm{in}\:\mathrm{a}\:\mathrm{15}×\mathrm{15}\:\mathrm{square}\right) \\ $$

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