Some elementary trig actually shows the correct answer (to the nearest whole degree and knot) to be 124deg/22kts.
But these are very acute angles, and the wizz-wheel simply won't be that accurate.
To see why, using the confuser's answer for W/V 131deg/21kts to achieve a track of 141deg and a G/S of 101kts, the required heading and TAS are (to the nearest whole degree and knot): 139deg/122kts, i.e. only 1deg and 1kt difference from the data provided.