Friendly Wager (July 2026 Challenge Question)

Since 2 to the 10 is 1024. Ten questions, each one asking above or below a halfway point, narrows it to one number.

So the odds are pretty good if he's smart. My first question would be if the number in question was equal to or above 512.

Let your guess of the unknown number N=512*A+256*B+128*C+64*D+32*E+16*F+8*G+4*H+2*I+J, where A thru J are 0 or 1.

Start with A, B, ... J =0;

(1) Set A=1. Ask if N is less than the number. If yes leave A=1, else reset it to 0 and recalculate N.

(2) Set B=1. Ask if N is less than the number. If yes leave B=1, else reset it to 0 and recalculate N.

(3) Set C=1. Ask if N is less than the number. If yes leave C=1, else reset it to 0 and recalculate N.

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(10) Set J=1. Ask if N is less than the number. If yes leave J=1, else reset it to 0 and recalculate N.

10 questions will determine A thru J and the value N.

A successive approximation analog-to-digital converter uses this principle to convert a voltage to a binary value. The successive approximation register (SAR) sets the bits one at a time, the digital-to-analog converter (DAC) converts its output to a voltage, and the comparator determines whether the voltage is too low or too high. If too low, the SAR sets that bit high for the next iteration.

https://en.wikipedia.org/wiki/Successive-approximation_ADC