Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 664 · 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 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) 72 (c) 8 (d) 27
2. 2.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) 7 (c) 63 (d) 24
3. 3.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 300 (c) 272 (d) 301
4. 4.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) 21 (c) 18 (d) 54
5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
6. 6.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) 19 (b) 171 (c) 60 (d) 57
7. 7.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) 63 (d) 189
8. 8.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) 20 (b) 60 (c) 180 (d) 63
9. 9.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 188 (c) 179 (d) 180
10. 10.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 588 (c) 598 (d) 597
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 14 (c) 16 (d) 4
12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 16 (c) 15 (d) 17
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 17 (c) 16 (d) 5
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 12 (c) 13 (d) 10
15. 15.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) 104 (c) 114 (d) 113
16. 16.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 7 (c) 6 (d) 5
18. 18.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
19. 19.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 96 (c) 87 (d) 78
20. 20.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
21. 21.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 489 (c) 480 (d) 490
22. 22.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 15 (b) 14 (c) 4 (d) 16
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 9 (d) 20
25. 25.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 3 (d) 5
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
29. 29.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 315 (d) 282
30. 30.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) 11 (b) 99 (c) 33 (d) 36
31. 31.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 318 (c) 309 (d) 319
32. 32.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 126 (c) 118 (d) 108
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 7 (c) 13 (d) 11
34. 34.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 252 (c) 246 (d) 261
35. 35.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 164 (d) 155
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 14 (d) 4
37. 37.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 5 (c) 10 (d) 7
39. 39.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) 69 (b) 207 (c) 23 (d) 72
40. 40.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) 51 (b) 17 (c) 54 (d) 153

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