Problem 57487. Compute the largest number with a given integer complexity

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; "><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; "><span style="">Cody Problems </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/42831"><span style=""><span style="text-decoration-line: underline; ">42831</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; "><span style=""> and </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/42834"><span style=""><span style="text-decoration-line: underline; ">42834</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 271.742px 8px; transform-origin: 271.742px 8px; unicode-bidi: normal; "><span style=""> ask us to compute integer complexity, the smallest number of 1s needed to construct a number with addition and multiplication. For example, the integer complexity of 11 is 8 because it can be written as </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="(1+1)x(1+1+1+1+1)+1" style="width: 204.5px; height: 18.5px;" width="204.5" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 259.817px 8px; transform-origin: 259.817px 8px; unicode-bidi: normal; "><span style="">. The other numbers with integer complexity 8 are 13, 14, 15, 16, and 18. Therefore </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="18 = (1+1+1)x(1+1+1)x(1+1)" style="width: 249px; height: 18.5px;" width="249" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.133px 8px; transform-origin: 122.133px 8px; unicode-bidi: normal; "><span style=""> is the largest integer with complexity 8.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.283px 8px; transform-origin: 366.283px 8px; unicode-bidi: normal; "><span style="">Write a function to determine the largest number with given integer complexities. Return the answers as a cell array of strings. </span></span></div></div></div>

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Problem 57487. Compute the largest number with a given integer complexity

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Problem 57487. Compute the largest number with a given integer complexity

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