Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 926 · 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.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 357 (c) 310 (d) 358
2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
4. 4.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) 72 (b) 24 (c) 8 (d) 27
5. 5.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 158 (c) 148 (d) 166
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
7. 7.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 216 (d) 72
8. 8.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
9. 9.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 272 (c) 301 (d) 291
10. 10.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 597 (d) 588
11. 11.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) 297 (c) 307 (d) 276
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
13. 13.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 69 (c) 207 (d) 72
14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 8 (d) 17
15. 15.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
17. 17.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 95 (c) 86 (d) 104
18. 18.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 72 (d) 54
19. 19.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
20. 20.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 265 (c) 255 (d) 264
21. 21.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 80 (c) 70 (d) 88
22. 22.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 135 (d) 48
23. 23.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 300 (c) 310 (d) 309
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
26. 26.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 511 (c) 501 (d) 510
27. 27.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 171 (c) 162 (d) 180
28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 5 (d) 7
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 16 (b) 18 (c) 7 (d) 17
31. 31.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
32. 32.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 386 (c) 462 (d) 471
33. 33.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 199 (d) 198
34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 4 (d) 15
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 3 (d) 4
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
40. 40.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) 9 (b) 30 (c) 27 (d) 81

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