Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 47 · 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 two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
2. 2.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 537 (d) 546
3. 3.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) 21 (c) 189 (d) 63
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
5. 5.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 345 (c) 355 (d) 354
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
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) 23 (b) 207 (c) 69 (d) 72
8. 8.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) 48 (d) 135
9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13
10. 10.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 74 (c) 56 (d) 66
11. 11.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
12. 12.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 394 (c) 484 (d) 474
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) 48 (b) 51 (c) 144 (d) 16
14. 14.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 358 (c) 429 (d) 430
15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 7 (d) 5
16. 16.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
17. 17.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
18. 18.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) 36 (b) 33 (c) 99 (d) 11
19. 19.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) 5 (b) 18 (c) 15 (d) 45
20. 20.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 135 (c) 136 (d) 144
21. 21.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 31 (c) 40 (d) 22
22. 22.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 194 (c) 185 (d) 176
23. 23.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
24. 24.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) 42 (d) 117
25. 25.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
26. 26.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 18 (c) 57 (d) 54
27. 27.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
28. 28.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
29. 29.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
30. 30.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) 14 (b) 126 (c) 42 (d) 45
31. 31.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 17 (d) 6
33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
34. 34.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
35. 35.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 270 (d) 298
36. 36.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) 216 (c) 72 (d) 24
37. 37.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 290 (c) 328 (d) 327
38. 38.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) 132 (c) 122 (d) 131
39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 4 (d) 5
40. 40.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 114 (d) 104

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