Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 52 · 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 4 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 16 (d) 17
2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
3. 3.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 472 (c) 601 (d) 591
4. 4.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) 8 (b) 72 (c) 24 (d) 27
5. 5.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
6. 6.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 143 (c) 144 (d) 152
7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
8. 8.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) 54 (c) 18 (d) 57
9. 9.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) 16 (c) 144 (d) 51
10. 10.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) 81 (d) 9
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 4 (b) 7 (c) 6 (d) 5
12. 12.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
13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
14. 14.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 582 (d) 460
15. 15.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) 18 (b) 45 (c) 5 (d) 15
16. 16.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 19 (d) 18
18. 18.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 559 (c) 549 (d) 444
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 6 (b) 7 (c) 9 (d) 10
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 3 (b) 5 (c) 4 (d) 6
21. 21.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 222 (c) 220 (d) 213
22. 22.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 408 (c) 399 (d) 409
23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 6 (d) 5
24. 24.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
26. 26.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
27. 27.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 597 (c) 607 (d) 476
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 10 (c) 12 (d) 13
29. 29.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 222 (c) 232 (d) 226
30. 30.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
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 20 (b) 8 (c) 19 (d) 18
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 16
33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 5 (b) 15 (c) 17 (d) 16
35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 16
36. 36.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 394 (c) 334 (d) 384
37. 37.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
38. 38.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 162 (c) 171 (d) 180
39. 39.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) 6 (b) 54 (c) 18 (d) 21
40. 40.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) 126 (b) 14 (c) 42 (d) 45

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