Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 643 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 19 (c) 20 (d) 9
2. 2.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 36 (d) 99
3. 3.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
4. 4.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 30 (d) 9
5. 5.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 15 (c) 5 (d) 45
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 15 (d) 14
7. 7.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 21 (d) 63
8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
9. 9.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 334 (d) 333
10. 10.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
11. 11.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 577 (c) 567 (d) 576
12. 12.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 481 (c) 480 (d) 392
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 12 (d) 14
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
16. 16.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 182 (d) 172
17. 17.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 270 (d) 271
18. 18.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
19. 19.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 45 (d) 14
20. 20.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 154 (c) 144 (d) 162
21. 21.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 276 (c) 307 (d) 297
22. 22.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 390 (c) 478 (d) 468
23. 23.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 39 (c) 117 (d) 42
24. 24.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 296 (d) 327
25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
26. 26.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 27 (d) 72
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 18 (d) 20
28. 28.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 91 (c) 92 (d) 82
29. 29.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 507 (c) 498 (d) 410
30. 30.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 158 (d) 168
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
32. 32.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 140 (d) 149
33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
34. 34.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 477 (c) 487 (d) 486
35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 13 (c) 12 (d) 5
36. 36.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 478 (d) 609
37. 37.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 24 (d) 7
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 14 (d) 13
39. 39.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
40. 40.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 492 (c) 406 (d) 501

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