This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 27

1971 Bundeswettbewerb Mathematik, 1
Tags: induction , invariant , arithmetic series , modular arithmetic
The numbers $1,2,...,1970$ are written on a board. One is allowed to remove $2$ numbers and to write down their difference instead. When repeated often enough, only one number remains. Show that this number is odd.

1990 AMC 12/AHSME, 13
Tags: arithmetic series
If the following instructions are carried out by a computer, which of $X$ will be printed because of instruction $5$? $1.$ Start $X$ at $3$ and $S$ at $0$ $2.$ Increase the value of $X$ by $2$. $3.$ Increase the value of $S$ by the value of $X$. $4.$ If $S$ is at least $10000$, then go to instsruction $5$; otherwise, go to instruction $2$ and proceed from there. $5.$ Print the value of $X$. $6.$ Stop. $\text{(A)} \ 19 \qquad \text{(B)} \ 21 \qquad \text{(C)} \ 23 \qquad \text{(D)} \ 199 \qquad \text{(E)} \ 201$