Problem Set

Problemset

No.	Problem	Tag
488	Given the three numbers Algebra
487	Convex polygons Geometry
486	In this diagram, not drawn to scale, Figures&nb...	Geometry
485	$A$ Algebra
484	A number Number Theory
483	With Algebra
482	In this diagram the center of the circle is&nbs...	Geometry
481	The measures of the interior angles of a convex...	Geometry
480	If $$f(n)=\tfrac{1}{3} n(n+1)(n+2... </a></td> <td> <span class=$ Algebra
479	Define an operation $\star$	Algebra
478	A straight line passing through the point ...	Geometry
477	If an arc of $60^{\circ}$	Geometry
476	Find the sum of all prime numbers between ...	Number Theory
475	The number halfway between Algebra
474	Which of the following statements is false? ...	Geometry
473	What is the sum of the digits of the decimal fo...	Number Theory
472	Problem 28 A circular disc with dia...	Geometry
471	If an arc of $60^{\circ}$	Geometry
470	If $$f(n)=\tfrac{1}{3} n(n+1)(n+2... </a></td> <td> <span class=$ Algebra
469	A positive number is mistakenly divided by ...	Number Theory
468	If an arc of $60^{\circ}$	Geometry
467	A triangle has angles of $$30^\ci... </a></td> <td> <span class=$ Trigonometry
466	In $\triangle ABC$	Geometry
465	Let $$\omega = \cos\frac{2\pi}{7}... </a></td> <td> <span class=$ Algebra
464	Consider the L-shaped region formed by three un...	Probability
463	A cube-shaped container has vertices	Geometry
462	Let Trigonometry
460	Let Algebra
459	In the accompanying figure, the outer square&nb...	Geometry
458	Define an operation $\star$	Algebra
457	A straight line passing through the point ...	Geometry
456	The real value of Algebra
455	A number Number Theory
454	Let Combinatorics Number Theory Probability
453	Sixteen chairs are arranged in...	Combinatorics
452	Let ${\triangle ABC}$ Algebra Geometry
451	There are exactly three positive real numbers&n...	Algebra
450	Find the number of collections...	Combinatorics
449	...	Algebra
448	...	Algebra
447	Let Trigonometry
446	For each positive integer,	Number Theory
445	Let	Algebra
444	Equilateral triangle	Geometry
443	Find the arithmetic mean of all the three-digit...	Number Theory
442	In the accompanying figure, the outer square&nb...	Geometry
441	For any finite set Combinatorics
440	For positive real numbers	Algebra Geometry
439	There are real numbers Algebra
438	Equilateral triangle	Geometry
437	Equilateral triangle	Geometry
436	Regular polygons with	Combinatorics
435	cube is constructed from Combinatorics
434	What is the average number of pairs of consecut...	Combinatorics Probability
433	For Number Theory
432	Find the number of ordered pairs of integers&nb...	Combinatorics Number Theory
431	A straight river that is	Algebra Geometry
430	Find the three-digit positive integer	Number Theory
429	Quadratic polynomials	Algebra
428	Let Geometry
427	Let Number Theory
426	Define $$f(x)=\|\| x\|-\tfrac{1}{2}\|... </a></td> <td> <span class=$ Algebra
425	Each vertex of a regular octagon is independent...	Combinatorics
424	Let $\triangle ABC$	Geometry
423	Let Geometry
422	Eight circles of radius	Geometry
421	Consider the paths of length Combinatorics
420	Rectangles	Geometry
419	Alice and Bob play the following game. A stack ...	Combinatorics
418	There exist real numbers	Algebra
417	Every morning Aya goes for a Algebra
416	When the roots of the polynomial	Algebra
415	You are playing a game. A $$2 \ti... </a></td> <td> <span class=$ Combinatorics
414	Let $\mathcal{B}$	Geometry
413	Let Combinatorics Number Theory
412	Carlos went to a sports store to buy running sh...	Algebra
411	Let Geometry
410	Alex divides a disk into four quadrants with tw...	Combinatorics Geometry Probability
409	The set of points in	Geometry Inequalities
408	A piecewise linear function is defined by	Algebra Geometry
407	The Combinatorics
406	The parabola with equation Algebra Geometry
405	The twelve letters Combinatorics Probability
404	An isosceles trapezoid has an inscribed circle ...	Geometry
403	here are Combinatorics Number Theory
402	Find the number of ordered pairs	Algebra
401	Find the sum of all integer bases	Number Theory
400	The numbers of apples growing on each of six ap...	Algebra
399	Let Algebra Combinatorics
398	Circles $\omega_1$	Algebra Geometry
397	Each vertex of a regular dodecagon (Combinatorics Geometry
396	Consider the L-shaped region formed by three un...	Geometry Probability
395	Let Algebra
394	Let Algebra
393	Recall that a palindrome is a number that reads...	Algebra Combinatorics
392	Define the sequence Algebra
391	There are $2^{10} = 1024$	Combinatorics
390	Let Algebra
389	Steve says to Jon, "I am thinking of a pol...	Algebra
388	The repeating decimals $$0.abab\o... </a></td> <td> <span class=$ Algebra

Problemset

Problem 28