Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 933 · 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.The numbers 15 to 23 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) 19 (c) 171 (d) 57
2. 2.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4
4. 4.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 16 (b) 15 (c) 17 (d) 6
6. 6.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) 432 (c) 441 (d) 366
7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 4 (d) 5
8. 8.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 456 (c) 576 (d) 567
9. 9.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 14 (d) 15
11. 11.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 376 (c) 457 (d) 447
12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 7 (b) 6 (c) 8 (d) 9
13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 3 (d) 6
14. 14.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
15. 15.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) 51 (b) 144 (c) 16 (d) 48
16. 16.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 622 (c) 486 (d) 612
17. 17.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 154 (c) 164 (d) 163
18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
19. 19.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) 24 (c) 7 (d) 63
20. 20.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 68 (c) 58 (d) 67
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) 39 (c) 42 (d) 117
22. 22.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) 75 (d) 24
23. 23.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) 54 (d) 57
24. 24.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 260 (c) 283 (d) 282
25. 25.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) 5 (c) 15 (d) 18
26. 26.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 415 (c) 405 (d) 414
27. 27.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 439 (b) 429 (c) 364 (d) 438
28. 28.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 445 (c) 368 (d) 444
29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
30. 30.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) 24 (b) 8 (c) 27 (d) 72
31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 8 (c) 18 (d) 19
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 5 (d) 2
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
35. 35.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 128 (c) 136 (d) 118
36. 36.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
38. 38.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) 33 (b) 36 (c) 11 (d) 99
39. 39.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
40. 40.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 108 (c) 100 (d) 90

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