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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 587 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 66 (d) 198
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 3 (d) 4
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 17 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  8. 8.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 129 (c) 130 (d) 138
  9. 9.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) 57 (b) 54 (c) 18 (d) 162
  10. 10.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) 27 (d) 24
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  12. 12.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 360 (c) 369 (d) 370
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 15 (d) 13
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 16 (d) 18
  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) 75 (b) 216 (c) 24 (d) 72
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
  17. 17.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 535 (d) 525
  18. 18.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 193 (d) 200
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 18 (d) 17
  21. 21.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 192 (c) 183 (d) 184
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 11 (c) 12 (d) 9
  24. 24.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 182 (c) 190 (d) 181
  25. 25.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 249 (d) 238
  26. 26.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) 20 (c) 63 (d) 180
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  28. 28.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) 315 (c) 306 (d) 282
  29. 29.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) 21 (b) 18 (c) 54 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  31. 31.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 220 (c) 210 (d) 219
  32. 32.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
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 11 (d) 3
  34. 34.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) 99 (b) 36 (c) 11 (d) 33
  35. 35.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 262 (c) 285 (d) 276
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
  37. 37.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) 33 (b) 10 (c) 30 (d) 90
  38. 38.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 128 (d) 127
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 18 (d) 19

Answer key

  1. 66
  2. 6
  3. 4
  4. 17
  5. 5
  6. 18
  7. 4
  8. 129
  9. 54
  10. 24
  11. 4
  12. 369
  13. 15
  14. 17
  15. 72
  16. 3
  17. 534
  18. 192
  19. 8
  20. 17
  21. 183
  22. 19
  23. 11
  24. 181
  25. 249
  26. 60
  27. 5
  28. 315
  29. 18
  30. 3
  31. 219
  32. 21
  33. 11
  34. 33
  35. 285
  36. 19
  37. 30
  38. 127
  39. 2
  40. 19

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