Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 699 · 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 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 267 (c) 250 (d) 258
2. 2.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 72 (c) 80 (d) 62
3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
4. 4.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 186 (c) 196 (d) 195
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 3 (d) 5
6. 6.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 56 (d) 55
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 9 (c) 10 (d) 3
8. 8.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
9. 9.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 384 (c) 328 (d) 375
10. 10.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) 160 (d) 151
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
12. 12.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 310 (c) 357 (d) 348
13. 13.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 522 (c) 523 (d) 513
14. 14.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 124 (c) 133 (d) 134
15. 15.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) 72 (c) 24 (d) 75
16. 16.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
17. 17.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
18. 18.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
20. 20.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) 60 (b) 63 (c) 20 (d) 180
21. 21.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 466 (c) 456 (d) 382
22. 22.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 59 (c) 68 (d) 60
23. 23.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
24. 24.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 136 (d) 126
25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 3 (d) 15
27. 27.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 273 (c) 283 (d) 260
28. 28.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 298 (c) 288 (d) 297
29. 29.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
30. 30.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) 81 (c) 27 (d) 30
31. 31.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 472 (c) 600 (d) 591
32. 32.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) 153 (c) 51 (d) 54
33. 33.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 373 (c) 363 (d) 372
34. 34.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 15 (c) 14 (d) 4
36. 36.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 366 (c) 432 (d) 441
37. 37.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) 135 (c) 45 (d) 48
38. 38.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) 27 (c) 24 (d) 8
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 17 (d) 19

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