Maths Olympiad Prep

Library /CEMC Gauss (Grade 8)

CEMC Gauss (Grade 8)

525 problems here, rated 1 to 4.9 on our scale (Junior to AIME). 1 of them ask for a proof. Years covered: 1998–2026.

Algebra 298Combinatorics 47Geometry 110Number theory 70
#TopicDiffTypeYear
1 Algebra 1.0 answer 1999 open
2 Algebra 1.0 answer 2004 open
3 Algebra 1.0 answer 2003 open
4 Algebra 1.0 answer 2000 open
5 Algebra 1.0 answer 2004 open
6 Number theory 1.0 answer 2006 open
7 Algebra 1.0 answer 2008 open
8 Algebra 1.0 answer 2011 open
9 Geometry 1.0 answer 2008 open
10 Algebra 1.0 answer 1999 open
11 Algebra 1.0 answer 2009 open
12 Algebra 1.0 answer 2005 open
13 Algebra 1.0 answer 2009 open
14 Algebra 1.0 answer 2001 open
15 Geometry 1.0 answer 2010 open
16 Number theory 1.0 answer 2007 open
17 Algebra 1.0 answer 1998 open
18 Algebra 1.0 answer 2002 open
19 Algebra 1.0 answer 1998 open
20 Algebra 1.0 answer 2007 open
21 Geometry 1.0 answer 2009 open
22 Algebra 1.0 answer 2003 open
23 Algebra 1.0 answer 2011 open
24 Algebra 1.0 answer 2000 open
25 Number theory 1.0 answer 2006 open
26 Algebra 1.0 answer 1999 open
27 Algebra 1.0 answer 2010 open
28 Number theory 1.0 answer 1999 open
29 Algebra 1.0 answer 2001 open
30 Number theory 1.0 answer 2001 open
31 Algebra 1.0 answer 2010 open
32 Algebra 1.0 answer 2001 open
33 Geometry 1.0 answer 2005 open
34 Algebra 1.0 answer 2008 open
35 Geometry 1.0 answer 2008 open
36 Algebra 1.0 answer 1999 open
37 Algebra 1.0 answer 2004 open
38 Geometry 1.0 answer 2004 open
39 Algebra 1.0 answer 2004 open
40 Algebra 1.0 answer 2008 open
41 Number theory 1.0 answer 1999 open
42 Algebra 1.0 answer 2004 open
43 Algebra 1.0 answer 2008 open
44 Algebra 1.0 answer 2002 open
45 Algebra 1.0 answer 2003 open
46 Algebra 1.0 answer 2005 open
47 Algebra 1.0 answer 2002 open
48 Number theory 1.0 answer 2002 open
49 Geometry 1.0 answer 2005 open
50 Algebra 1.0 answer 2007 open
51 Algebra 1.0 answer 2004 open
52 Algebra 1.0 answer 2008 open
53 Combinatorics 1.0 answer 2001 open
54 Algebra 1.0 answer 2006 open
55 Geometry 1.0 answer 2008 open
56 Algebra 1.0 answer 2003 open
57 Algebra 1.0 answer 2001 open
58 Number theory 1.0 answer 2002 open
59 Algebra 1.0 answer 1999 open
60 Algebra 1.0 answer 2011 open
61 Combinatorics 1.0 answer 2010 open
62 Geometry 1.0 answer 2005 open
63 Algebra 1.0 answer 2006 open
64 Geometry 1.0 answer 2003 open
65 Algebra 1.0 answer 2003 open
66 Number theory 1.0 answer 1998 open
67 Geometry 1.0 answer 2002 open
68 Geometry 1.0 answer 1999 open
69 Algebra 1.0 answer 2001 open
70 Algebra 1.0 answer 2003 open
71 Algebra 1.0 answer 2003 open
72 Algebra 1.0 answer 2010 open
73 Algebra 1.0 answer 2007 open
74 Algebra 1.0 answer 2004 open
75 Algebra 1.0 answer 2008 open
76 Algebra 1.0 answer 1998 open
77 Algebra 1.0 answer 2007 open
78 Algebra 1.0 answer 2006 open
79 Number theory 1.0 answer 2001 open
80 Algebra 1.0 answer 2010 open
81 Algebra 1.0 answer 2010 open
82 Algebra 1.0 answer 2011 open
83 Algebra 1.0 answer 2010 open
84 Geometry 1.0 answer 2008 open
85 Algebra 1.0 answer 2000 open
86 Combinatorics 1.0 answer 2011 open
87 Algebra 1.0 answer 2005 open
88 Algebra 1.0 answer 1999 open
89 Algebra 1.0 answer 2002 open
90 Algebra 1.0 answer 2009 open
91 Algebra 1.0 answer 2005 open
92 Number theory 1.0 answer 2000 open
93 Geometry 1.0 answer 2008 open
94 Algebra 1.0 answer 2000 open
95 Algebra 1.0 answer 2003 open
96 Algebra 1.0 answer 2009 open
97 Algebra 1.0 answer 2011 open
98 Algebra 1.0 answer 2006 open
99 Algebra 1.0 answer 2004 open
100 Geometry 1.0 answer 2001 open
101 Algebra 1.0 answer 1998 open
102 Algebra 1.0 answer 2004 open
103 Algebra 1.0 answer 2011 open
104 Algebra 1.0 answer 2007 open
105 Algebra 1.0 answer 2000 open
106 Algebra 1.0 answer 2008 open
107 Algebra 1.0 answer 2005 open
108 Algebra 1.0 answer 2010 open
109 Algebra 1.0 answer 2004 open
110 Combinatorics 1.0 answer 1998 open
111 Algebra 1.0 answer 2005 open
112 Algebra 1.0 answer 2011 open
113 Algebra 1.0 answer 2007 open
114 Algebra 1.0 answer 2008 open
115 Combinatorics 1.0 answer 2002 open
116 Algebra 1.0 answer 2005 open
117 Algebra 1.0 answer 2002 open
118 Algebra 1.0 answer 2006 open
119 Algebra 1.0 answer 2005 open
120 Algebra 1.0 answer 2003 open
121 Algebra 1.0 answer 1998 open
122 Number theory 1.0 answer 2008 open
123 Algebra 1.0 answer 2004 open
124 Algebra 1.0 answer 2008 open
125 Algebra 1.0 answer 2001 open
126 Algebra 1.0 answer 2010 open
127 Algebra 1.0 answer 1998 open
128 Algebra 1.0 answer 2010 open
129 Algebra 1.0 answer 2002 open
130 Algebra 1.0 answer 2010 open
131 Algebra 1.0 answer 2011 open
132 Algebra 1.0 answer 1998 open
133 Geometry 1.0 answer 2011 open
134 Number theory 1.0 answer 2002 open
135 Algebra 1.0 answer 2009 open
136 Algebra 1.0 answer 2000 open
137 Geometry 1.0 answer 1998 open
138 Number theory 1.0 answer 1999 open
139 Algebra 1.0 answer 2004 open
140 Algebra 1.0 answer 2005 open
141 Algebra 1.0 answer 2009 open
142 Algebra 1.0 answer 2006 open
143 Algebra 1.0 answer 2007 open
144 Number theory 1.0 answer 2002 open
145 Algebra 1.0 answer 2010 open
146 Algebra 1.0 answer 2003 open
147 Algebra 1.0 answer 2001 open
148 Algebra 1.0 answer 2010 open
149 Number theory 1.0 answer 2002 open
150 Algebra 1.0 answer 2000 open
151 Number theory 1.0 answer 2002 open
152 Algebra 1.0 answer 2011 open
153 Geometry 1.0 answer 2006 open
154 Algebra 1.0 answer 2000 open
155 Algebra 1.0 answer 1998 open
156 Algebra 1.0 answer 2011 open
157 Algebra 1.0 answer 2002 open
158 Algebra 1.0 answer 2009 open
159 Number theory 1.0 answer 2006 open
160 Number theory 1.0 answer 1999 open
161 Geometry 1.0 answer 2007 open
162 Algebra 1.0 answer 2006 open
163 Algebra 1.0 answer 1998 open
164 Algebra 1.0 answer 2006 open
165 Algebra 1.0 answer 2005 open
166 Algebra 1.0 answer 2010 open
167 Geometry 1.0 answer 2005 open
168 Algebra 1.0 answer 1999 open
169 Algebra 1.0 answer 2007 open
170 Algebra 1.0 answer 2001 open
171 Algebra 1.0 answer 2000 open
172 Algebra 1.0 answer 2004 open
173 Algebra 1.0 answer 2009 open
174 Geometry 1.0 answer 1998 open
175 Algebra 1.0 answer 2002 open
176 Algebra 1.0 answer 2008 open
177 Algebra 1.0 answer 1999 open
178 Algebra 1.0 answer 2009 open
179 Algebra 1.0 answer 2010 open
180 Algebra 1.0 answer 2005 open
181 Algebra 1.0 answer 2001 open
182 Number theory 1.0 answer 2005 open
183 Algebra 1.0 answer 1999 open
184 Number theory 1.0 answer 2008 open
185 Geometry 1.0 answer 2009 open
186 Algebra 1.0 answer 2002 open
187 Number theory 1.0 answer 2004 open
188 Algebra 1.0 answer 2002 open
189 Algebra 1.0 answer 2007 open
190 Combinatorics 1.0 answer 1999 open
191 Algebra 1.0 answer 2000 open
192 Geometry 1.0 answer 2003 open
193 Algebra 1.0 answer 2007 open
194 Combinatorics 1.0 answer 2025 open
195 Algebra 1.0 answer 2026 open
196 Algebra 1.0 answer 2017 open
197 Algebra 1.0 answer 2023 open
198 Algebra 1.0 answer 2020 open
199 Algebra 1.0 answer 2018 open
200 Number theory 1.0 answer 2024 open
201 Algebra 1.0 answer 2012 open
202 Algebra 1.0 answer 2019 open
203 Algebra 1.1 answer 2017 open
204 Algebra 1.1 answer 2026 open
205 Algebra 1.1 answer 2020 open
206 Algebra 1.1 answer 2015 open
207 Algebra 1.1 answer 2018 open
208 Algebra 1.1 answer 2013 open
209 Algebra 1.1 answer 2023 open
210 Combinatorics 1.1 answer 2022 open
211 Algebra 1.1 answer 2014 open
212 Algebra 1.1 answer 2018 open
213 Algebra 1.1 answer 2014 open
214 Algebra 1.1 answer 2024 open
215 Geometry 1.1 answer 2026 open
216 Algebra 1.1 answer 2020 open
217 Algebra 1.1 answer 2022 open
218 Algebra 1.1 answer 2025 open
219 Algebra 1.1 answer 2013 open
220 Number theory 1.1 answer 2023 open
221 Algebra 1.1 answer 2012 open
222 Combinatorics 1.1 answer 2017 open
223 Algebra 1.1 answer 2022 open
224 Algebra 1.1 answer 2017 open
225 Algebra 1.1 answer 2025 open
226 Geometry 1.1 answer 2014 open
227 Geometry 1.1 answer 2012 open
228 Algebra 1.1 answer 2018 open
229 Algebra 1.1 answer 2020 open
230 Number theory 1.1 answer 2019 open
231 Algebra 1.1 answer 2024 open
232 Algebra 1.1 answer 2026 open
233 Algebra 1.1 answer 2023 open
234 Algebra 1.2 answer 2017 open
235 Algebra 1.2 answer 2013 open
236 Algebra 1.2 answer 2015 open
237 Algebra 1.2 answer 2022 open
238 Algebra 1.2 answer 2026 open
239 Geometry 1.2 answer 2020 open
240 Algebra 1.2 answer 2012 open
241 Algebra 1.2 answer 2023 open
242 Number theory 1.2 answer 2019 open
243 Algebra 1.2 answer 2014 open
244 Combinatorics 1.2 answer 2025 open
245 Geometry 1.2 answer 2026 open
246 Algebra 1.2 answer 2012 open
247 Algebra 1.2 answer 2018 open
248 Geometry 1.2 answer 2015 open
249 Algebra 1.2 answer 2024 open
250 Algebra 1.2 answer 2013 open
251 Combinatorics 1.2 answer 2019 open
252 Number theory 1.2 answer 2020 open
253 Algebra 1.2 answer 2012 open
254 Number theory 1.2 answer 2014 open
255 Algebra 1.2 answer 2022 open
256 Algebra 1.2 answer 2024 open
257 Algebra 1.2 answer 2015 open
258 Geometry 1.2 answer 2018 open
259 Algebra 1.2 answer 2017 open
260 Algebra 1.2 answer 2023 open
261 Algebra 1.2 answer 2026 open
262 Algebra 1.3 answer 2023 open
263 Combinatorics 1.3 answer 2026 open
264 Algebra 1.3 answer 2022 open
265 Algebra 1.3 answer 2013 open
266 Algebra 1.3 answer 2018 open
267 Algebra 1.3 answer 2015 open
268 Algebra 1.3 answer 2017 open
269 Algebra 1.3 answer 2020 open
270 Geometry 1.3 answer 2014 open
271 Algebra 1.3 answer 2022 open
272 Algebra 1.3 answer 2015 open
273 Combinatorics 1.3 answer 2020 open
274 Geometry 1.3 answer 2013 open
275 Algebra 1.3 answer 2017 open
276 Algebra 1.3 answer 2023 open
277 Algebra 1.3 answer 2014 open
278 Number theory 1.3 answer 2024 open
279 Algebra 1.3 answer 2012 open
280 Algebra 1.4 answer 2018 open
281 Algebra 1.4 answer 2014 open
282 Number theory 1.4 answer 2026 open
283 Number theory 1.4 answer 2019 open
284 Geometry 1.4 answer 2022 open
285 Algebra 1.4 answer 2015 open
286 Geometry 1.4 answer 2023 open
287 Algebra 1.4 answer 2013 open
288 Algebra 1.4 answer 2020 open
289 Algebra 1.4 answer 2017 open
290 Algebra 1.4 answer 2013 open
291 Algebra 1.4 answer 2025 open
292 Geometry 1.4 answer 2015 open
293 Algebra 1.4 answer 2018 open
294 Algebra 1.4 answer 2026 open
295 Algebra 1.4 answer 2015 open
296 Algebra 1.4 answer 2025 open
297 Algebra 1.4 answer 2012 open
298 Geometry 1.4 answer 2014 open
299 Number theory 1.4 answer 2024 open
300 Algebra 1.4 answer 2018 open
301 Algebra 1.4 answer 2017 open
302 Algebra 1.4 answer 2026 open
303 Geometry 1.4 answer 2015 open
304 Algebra 1.4 answer 2022 open
305 Algebra 1.4 answer 2025 open
306 Algebra 1.4 answer 2020 open
307 Algebra 1.4 answer 2018 open
308 Algebra 1.5 answer 2024 open
309 Algebra 1.5 answer 2019 open
310 Number theory 1.5 answer 2018 open
311 Algebra 1.5 answer 2012 open
312 Geometry 1.5 answer 2020 open
313 Combinatorics 1.5 answer 2019 open
314 Geometry 1.5 answer 2023 open
315 Number theory 1.5 answer 2013 open
316 Geometry 1.5 answer 2014 open
317 Number theory 1.5 answer 2024 open
318 Combinatorics 1.6 answer 2022 open
319 Algebra 1.6 answer 2012 open
320 Algebra 1.6 answer 2023 open
321 Algebra 1.6 answer 2022 open
322 Algebra 1.6 answer 2019 open
323 Algebra 1.6 answer 2018 open
324 Geometry 1.6 answer 2013 open
325 Algebra 1.6 answer 2018 open
326 Algebra 1.6 answer 2013 open
327 Algebra 1.6 answer 2022 open
328 Algebra 1.6 answer 2017 open
329 Geometry 1.6 answer 2012 open
330 Algebra 1.6 answer 2015 open
331 Geometry 1.6 answer 2024 open
332 Algebra 1.7 answer 2014 open
333 Algebra 1.7 answer 2020 open
334 Algebra 1.7 answer 2017 open
335 Algebra 1.7 answer 2025 open
336 Algebra 1.7 answer 2012 open
337 Algebra 1.8 answer 2023 open
338 Algebra 1.8 answer 2014 open
339 Geometry 2.0 proof 1998 open
340 Algebra 2.0 answer 2010 open
341 Algebra 2.0 answer 2011 open
342 Geometry 2.0 answer 2009 open
343 Geometry 2.0 answer 2000 open
344 Algebra 2.0 answer 2010 open
345 Geometry 2.0 answer 1998 open
346 Algebra 2.0 answer 2011 open
347 Algebra 2.0 answer 2001 open
348 Algebra 2.0 answer 2000 open
349 Number theory 2.0 answer 2008 open
350 Geometry 2.0 answer 2000 open
351 Geometry 2.0 answer 2000 open
352 Number theory 2.0 answer 2000 open
353 Combinatorics 2.0 answer 2001 open
354 Number theory 2.0 answer 2006 open
355 Number theory 2.0 answer 2006 open
356 Algebra 2.0 answer 2003 open
357 Geometry 2.0 answer 2009 open
358 Number theory 2.0 answer 2004 open
359 Number theory 2.0 answer 2003 open
360 Combinatorics 2.0 answer 2009 open
361 Algebra 2.0 answer 2003 open
362 Number theory 2.0 answer 1999 open
363 Algebra 2.0 answer 2007 open
364 Algebra 2.0 answer 2007 open
365 Number theory 2.0 answer 2007 open
366 Algebra 2.0 answer 1999 open
367 Geometry 2.0 answer 2005 open
368 Geometry 2.0 answer 1999 open
369 Algebra 2.0 answer 1998 open
370 Geometry 2.0 answer 1999 open
371 Combinatorics 2.0 answer 2003 open
372 Geometry 2.0 answer 2007 open
373 Combinatorics 2.0 answer 2009 open
374 Number theory 2.0 answer 2000 open
375 Combinatorics 2.0 answer 2011 open
376 Combinatorics 2.0 answer 2003 open
377 Geometry 2.0 answer 2004 open
378 Combinatorics 2.0 answer 1998 open
379 Algebra 2.0 answer 2007 open
380 Geometry 2.0 answer 1999 open
381 Number theory 2.0 answer 2009 open
382 Combinatorics 2.0 answer 2009 open
383 Combinatorics 2.0 answer 1998 open
384 Geometry 2.0 answer 2008 open
385 Number theory 2.0 answer 2000 open
386 Number theory 2.0 answer 2011 open
387 Combinatorics 2.0 answer 2000 open
388 Algebra 2.0 answer 2010 open
389 Geometry 2.0 answer 2010 open
390 Geometry 2.0 answer 2000 open
391 Geometry 2.0 answer 2001 open
392 Combinatorics 2.0 answer 1998 open
393 Geometry 2.0 answer 2003 open
394 Algebra 2.0 answer 2006 open
395 Geometry 2.0 answer 2010 open
396 Geometry 2.0 answer 2010 open
397 Number theory 2.0 answer 2011 open
398 Geometry 2.0 answer 2006 open
399 Geometry 2.0 answer 2004 open
400 Algebra 2.0 answer 2002 open
401 Number theory 2.0 answer 2008 open
402 Combinatorics 2.0 answer 2006 open
403 Geometry 2.0 answer 2005 open
404 Number theory 2.0 answer 2001 open
405 Geometry 2.0 answer 2008 open
406 Geometry 2.0 answer 1998 open
407 Geometry 2.0 answer 2011 open
408 Geometry 2.0 answer 2007 open
409 Combinatorics 2.0 answer 1999 open
410 Algebra 2.0 answer 2003 open
411 Algebra 2.0 answer 1998 open
412 Geometry 2.0 answer 2006 open
413 Algebra 2.0 answer 2009 open
414 Geometry 2.0 answer 2004 open
415 Algebra 2.1 answer 2013 open
416 Geometry 2.3 answer 2019 open
417 Geometry 2.4 answer 2012 open
418 Geometry 2.4 answer 2023 open
419 Geometry 2.4 answer 2019 open
420 Geometry 2.4 answer 2023 open
421 Number theory 2.4 answer 2020 open
422 Geometry 2.4 answer 2017 open
423 Geometry 2.4 answer 2019 open
424 Algebra 2.5 answer 2019 open
425 Algebra 2.5 answer 2012 open
426 Algebra 2.5 answer 2014 open
427 Algebra 2.5 answer 2026 open
428 Combinatorics 2.5 answer 2015 open
429 Algebra 2.5 answer 2026 open
430 Algebra 2.5 answer 2025 open
431 Geometry 2.5 answer 2014 open
432 Algebra 2.5 answer 2025 open
433 Geometry 2.5 answer 2024 open
434 Number theory 2.6 answer 2015 open
435 Algebra 2.6 answer 2014 open
436 Algebra 2.6 answer 2026 open
437 Geometry 2.7 answer 2026 open
438 Algebra 2.7 answer 2018 open
439 Algebra 2.7 answer 2015 open
440 Algebra 2.7 answer 2024 open
441 Algebra 2.7 answer 2022 open
442 Algebra 2.7 answer 2012 open
443 Algebra 2.7 answer 2013 open
444 Number theory 2.7 answer 2026 open
445 Combinatorics 2.7 answer 2017 open
446 Algebra 2.7 answer 2020 open
447 Algebra 2.7 answer 2013 open
448 Geometry 2.7 answer 2015 open
449 Combinatorics 2.7 answer 2025 open
450 Algebra 2.7 answer 2018 open
451 Algebra 2.7 answer 2019 open
452 Geometry 2.8 answer 2013 open
453 Algebra 2.8 answer 2017 open
454 Algebra 2.8 answer 2022 open
455 Algebra 2.8 answer 2024 open
456 Algebra 2.8 answer 2015 open
457 Geometry 2.8 answer 2025 open
458 Algebra 2.9 answer 2013 open
459 Geometry 3.0 answer 1999 open
460 Geometry 3.0 answer 2003 open
461 Combinatorics 3.0 answer 2000 open
462 Combinatorics 3.0 answer 2011 open
463 Geometry 3.0 answer 1998 open
464 Number theory 3.0 answer 2009 open
465 Geometry 3.0 answer 2000 open
466 Algebra 3.0 answer 2011 open
467 Combinatorics 3.0 answer 2006 open
468 Number theory 3.0 answer 2010 open
469 Geometry 3.0 answer 2011 open
470 Geometry 3.0 answer 2009 open
471 Algebra 3.0 answer 2008 open
472 Algebra 3.0 answer 2005 open
473 Algebra 3.0 answer 1999 open
474 Number theory 3.0 answer 2005 open
475 Number theory 3.0 answer 2007 open
476 Geometry 3.0 answer 2005 open
477 Geometry 3.0 answer 2009 open
478 Number theory 3.0 answer 2001 open
479 Combinatorics 3.0 answer 2001 open
480 Geometry 3.0 answer 2011 open
481 Combinatorics 3.0 answer 1999 open
482 Geometry 3.0 answer 2003 open
483 Number theory 3.0 answer 2004 open
484 Geometry 3.0 answer 2002 open
485 Geometry 3.0 answer 2010 open
486 Geometry 3.0 answer 2004 open
487 Geometry 3.5 answer 2026 open
488 Geometry 3.5 answer 2020 open
489 Geometry 3.5 answer 2017 open
490 Algebra 3.6 answer 2020 open
491 Geometry 3.6 answer 2025 open
492 Geometry 3.7 answer 2018 open
493 Geometry 3.7 answer 2023 open
494 Combinatorics 3.8 answer 2020 open
495 Number theory 3.8 answer 2019 open
496 Geometry 3.8 answer 2014 open
497 Number theory 3.8 answer 2019 open
498 Algebra 3.8 answer 2015 open
499 Algebra 3.8 answer 2023 open
500 Combinatorics 3.8 answer 2012 open
501 Number theory 3.8 answer 2025 open
502 Algebra 3.8 answer 2013 open
503 Number theory 3.8 answer 2013 open
504 Number theory 3.8 answer 2026 open
505 Number theory 3.8 answer 2023 open
506 Combinatorics 3.8 answer 2025 open
507 Number theory 3.8 answer 2022 open
508 Geometry 3.9 answer 2012 open
509 Number theory 4.6 answer 2026 open
510 Number theory 4.7 answer 2017 open
511 Geometry 4.7 answer 2019 open
512 Geometry 4.8 answer 2026 open
513 Combinatorics 4.8 answer 2026 open
514 Geometry 4.8 answer 2020 open
515 Combinatorics 4.8 answer 2019 open
516 Algebra 4.8 answer 2015 open
517 Combinatorics 4.8 answer 2020 open
518 Combinatorics 4.8 answer 2012 open
519 Geometry 4.8 answer 2017 open
520 Combinatorics 4.8 answer 2024 open
521 Combinatorics 4.9 answer 2025 open
522 Number theory 4.9 answer 2014 open
523 Combinatorics 4.9 answer 2023 open
524 Combinatorics 4.9 answer 2017 open
525 Number theory 4.9 answer 2015 open
These are sorted by difficulty within the competition, but they aren't a course. The track is the route through, drawn from all the sources at once.