Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 403 · 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 7? (a) 8 (b) 6 (c) 10 (d) 7
2. 2.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 423 (c) 432 (d) 360
3. 3.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 453 (c) 380 (d) 462
4. 4.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
5. 5.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) 192 (c) 206 (d) 201
6. 6.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 129 (d) 120
7. 7.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 52 (d) 61
8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 17
9. 9.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
10. 10.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 189 (c) 180 (d) 198
11. 11.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
13. 13.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 561 (d) 446
14. 14.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
15. 15.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 397 (c) 396 (d) 387
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
17. 17.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) 216 (b) 24 (c) 72 (d) 75
18. 18.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 94 (c) 86 (d) 85
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16
20. 20.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 452 (c) 561 (d) 570
21. 21.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) 117 (c) 39 (d) 42
22. 22.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 358 (c) 348 (d) 310
23. 23.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
24. 24.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 113 (c) 114 (d) 104
25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
26. 26.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) 30 (b) 33 (c) 90 (d) 10
27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 3 (d) 2
28. 28.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) 15 (b) 45 (c) 48 (d) 135
29. 29.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 393 (c) 402 (d) 340
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 6 (d) 7
31. 31.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) 9 (d) 30
32. 32.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 220 (c) 222 (d) 223
33. 33.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 364 (c) 438 (d) 439
34. 34.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
35. 35.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 44 (c) 34 (d) 52
36. 36.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 243 (c) 234 (d) 351
37. 37.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) 18 (b) 21 (c) 6 (d) 54
38. 38.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
39. 39.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
40. 40.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 450 (d) 558

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