Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 760 · 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.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 198 (d) 66
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
3. 3.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 70 (d) 78
4. 4.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 513 (c) 414 (d) 504
5. 5.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 92 (d) 83
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 14 (c) 3 (d) 15
7. 7.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 408 (c) 344 (d) 409
8. 8.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
9. 9.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 180 (c) 170 (d) 179
10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 16 (d) 4
12. 12.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 313 (c) 303 (d) 280
13. 13.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 48 (c) 16 (d) 51
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 21
15. 15.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
16. 16.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) 24 (b) 72 (c) 27 (d) 8
17. 17.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
18. 18.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 396 (c) 336 (d) 397
19. 19.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 30 (c) 33 (d) 90
20. 20.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) 42 (b) 39 (c) 117 (d) 13
21. 21.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 110 (c) 102 (d) 92
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 5 (d) 16
23. 23.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 145 (d) 154
24. 24.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
25. 25.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 13 (c) 7 (d) 11
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 13 (d) 4
28. 28.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 459 (d) 450
29. 29.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 180 (c) 60 (d) 63
30. 30.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
31. 31.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 60 (d) 57
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 18 (b) 19 (c) 17 (d) 7
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 19 (d) 7
34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
36. 36.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
37. 37.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 130 (c) 112 (d) 122
38. 38.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 348 (d) 349
39. 39.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 469 (c) 468 (d) 384
40. 40.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 422 (c) 516 (d) 526

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