Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 902 · 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 5 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 17 (d) 15
2. 2.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
3. 3.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 420 (c) 358 (d) 429
4. 4.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 206 (c) 192 (d) 201
5. 5.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 372 (c) 450 (d) 441
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 15 (d) 16
7. 7.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) 72 (b) 207 (c) 23 (d) 69
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
9. 9.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) 45 (b) 18 (c) 15 (d) 5
10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
11. 11.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 294 (c) 324 (d) 333
12. 12.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 381 (c) 391 (d) 390
13. 13.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
15. 15.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 132 (d) 131
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 18 (d) 7
17. 17.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) 8 (c) 24 (d) 27
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 9 (c) 8 (d) 10
19. 19.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
20. 20.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 342 (c) 306 (d) 352
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 16 (c) 17 (d) 5
22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
23. 23.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) 51 (b) 17 (c) 54 (d) 153
24. 24.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) 27 (b) 30 (c) 9 (d) 81
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 19 (d) 18
26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 5 (c) 16 (d) 17
29. 29.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
30. 30.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) 21 (b) 189 (c) 63 (d) 66
31. 31.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) 63 (b) 21 (c) 24 (d) 7
32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
33. 33.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 456 (c) 382 (d) 465
34. 34.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 21 (d) 6
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 19 (d) 20
36. 36.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
37. 37.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 32 (d) 50
38. 38.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) 16 (c) 51 (d) 48
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 15 (b) 14 (c) 16 (d) 5
40. 40.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 384 (c) 469 (d) 459

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