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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 131 · 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 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) 144 (b) 16 (c) 48 (d) 51
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 5 (d) 4
  4. 4.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 52 (d) 43
  5. 5.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) 189 (b) 66 (c) 63 (d) 21
  6. 6.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 160 (c) 142 (d) 152
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  10. 10.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) 15 (c) 18 (d) 5
  11. 11.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 246 (d) 247
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  15. 15.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 416 (d) 516
  16. 16.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 553 (c) 543 (d) 552
  17. 17.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) 54 (d) 18
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  19. 19.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
  20. 20.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 396 (d) 397
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 6 (c) 5 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  25. 25.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) 24 (b) 21 (c) 7 (d) 63
  26. 26.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 428 (c) 534 (d) 535
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 7 (c) 4 (d) 6
  28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 550 (c) 540 (d) 549
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  30. 30.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 402 (c) 495 (d) 496
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  32. 32.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) 198 (d) 66
  33. 33.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) 23 (b) 207 (c) 72 (d) 69
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  36. 36.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 412 (c) 402 (d) 346
  37. 37.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 237 (c) 228 (d) 230
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6

Answer key

  1. 48
  2. 3
  3. 4
  4. 43
  5. 63
  6. 151
  7. 15
  8. 3
  9. 5
  10. 15
  11. 246
  12. 6
  13. 17
  14. 4
  15. 516
  16. 552
  17. 18
  18. 18
  19. 282
  20. 396
  21. 3
  22. 7
  23. 8
  24. 9
  25. 21
  26. 534
  27. 6
  28. 549
  29. 8
  30. 495
  31. 18
  32. 66
  33. 69
  34. 19
  35. 4
  36. 411
  37. 237
  38. 17
  39. 9
  40. 6

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