Thursday, 3 September 2015

Numbers 1,2,3,4 from 151 to 200

After my previous posts on using the digits 1,2,3,4 and mathematical operators (which, by the way, have become increasingly creative and powerful) to create the numbers 1-50, then 51-100 and 101 to 150, I'd like to present a team effort on the numbers from 151 to 200.  I didn't think it was possible.  In fact, I very much doubt that the authors of the maths textbook that posed the original idea thought it would be possible.  Nonetheless, here it is:  use the digits 1,2,3,4 and any mathematical operators you care to name to produce the totals from 151 to 200.

Credit to Denis from the freemathhelp forum for his work on this, providing the vast majority of the results and taking the problem way beyond its original scope.  Major credit also to Skipjack for providing the solutions marked with an asterisk.

To clarify, r(.1) = repeating decimal.

151: (4! + 3!) / .2 + 1
152: (1 + 4)! + 32
153: 34 / 2 / r(.1)
154: 2^4 / .1 - 3!
155: 31 * 2 / .4
156:4! * 3! + 12
157: 314 / 2
158: 3!! * .2 + 14
159: 3!! / 4 - 21
160: 32 * (1 + 4)
161: 3^4 * 2 - 1
162: 3^4 * 2 * 1
163: 3^4 * 2 + 1
164: (3! - 2) * 41
165: 4! + 3! + 21
*166: 4! * (3! + 1) - 2
167: 13^2 - SQRT(4)
168: 14 * 3! * 2
169: 13^(4 - 2)
170: 34 / .2 * 1
171: 13^2 + SQRT(4)
172 = .1^(-2) + 3 * 4!
173: 13^2 + 4
*174: 3! * (4! + 1 / .2)
175: 3!! / 4 - 1 / .2
*176: 4! / .1 - 2^3!
177: 3!! / 4 - 1 - 2
178: 3!! / 4 - 1 * 2
179: 3!! / 4 + 1 - 2
180: 3!! / 4 * (2 - 1)
181: 3!! / 4 - 1 + 2
182: 3!! / 4 + 1 * 2
183: 3!! / 4 + 1 + 2
184: 3!! * .2 + 4 / .1
185: 3!! * .2 + 41
186: (2 + 4) * 31
*187: (4! - 3) / r(.1) - 2
188 = (.1^(-2) - 3!) * SQRT(4)
189: 213 - 4!
190: 14^2 - 3!
191: 4! * 2^3 - 1
192: 3!! / 4 + 12
193: 14^2 - 3
194: 4 / .1 / .2 - 3!
195 = (4! - 2) / r(.1) - 3
*196: 4 * (3! + 1)^2
197: 4 / .1 / .2 - 3
198 = (3! * 4 - 2) / r(.1)
199: 14^2 + 3
200: (2 + 3) * 4 / .1

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