This mathematical series of puzzle caches has questions from all levels of school education, from Key Stage 1 (age 5-7) in the first few caches, all the way up to Further Maths A-Level in the last few caches. Everybody should be able to get the solutions to the first few caches, but how far through the series will you be able to get? For a full description of the series, please see the first cache “1+1=1”. If you can’t solve a particular set of questions, try asking somebody of the appropriate age, or your friendly neighbourhood Maths teacher!
Please note that many of the caches are hidden near busy roads, so please take care when finding them, especially if you have children with you. It is worth noting that there is parking possible within a few hundred metres of all caches and a quick look on a satellite view map should show suitable places.
This bonus cache contains questions from the Key Stages 3 & 4 caches, suitable for ages 11 - 16, school years 7 -11.
1. From 1+1=8. I started geocaching at 3pm. When I finished, the hour hand on my watch had turned through ninety degrees What time did I finish geocaching? A= the sum of the digits in your answer.
2. From 1+1=9. 3b-5=b+3. Find b.
3. From 1+1=10. I am thinking of a number. When I subtract 25 from my number and then square the answer, I get the same result as when I square my number and then subtract 25 from my answer. C=the sum of the digits in my number.
4. From 1+1=11. Luke has three times as many sisters as brothers. His sister Helen has twice as many sisters as brothers. D= the number of children in the family.
5. From 1+1=12. I painted my shed. I used half a 3 litre can on the first coat of paint, and two thirds of the remainder on the second coat. How much paint was left in the can after the second coat, in milliliters? E= the sum of the digits in your answer.
6. From 1+1=13. Peter is 50 years, 50 months, 50 weeks and 50 days old. What age will he be on his next birthday? F= the sum of the digits in your answer.
7. From 1+1=14. The positive root of the equation x^2+5x-2=0 is 0.37G to 3 decimal places. Find G.
8. From 1+1=15. (8-sqrt(18))/sqrt(2) = p + q x sqrt(2), H= p + q. (Where ‘x’ means times, and sqrt(18) means the square root of 18).
9. From 1+1=16. PQR is a triangle. PQ =8, angle PQR = 90 degrees, angle RPQ = 42 degrees. Find the length PR. J= your answer to the nearest whole number.
10. From 1+1=17. The sum ONE + FOUR = SEVENTY is correct if we replace each word with the number of letters in it, to give 3+4=7. Using the same idea, K= the lowest number that makes the following sum work: THREE + FIVE = ?
11. From 1+1=18. If 5^p=9, 9^q=12, 12^r=16, 16^s=20 and 20^t=25, L=p*q*r*s*t (* means multiply)
12. From 1+1=19. My cylindrical birthday cake this year wasn’t big enough, so next year I will double the radius and triple the height of the cake. What will be the ratio of the volume of next year’s birthday cake to the volume of this year’s cake, if written as M:1?
The cache can be found at N50 45.PQR E0 14.STU where P=A+B-C, Q=D-F, R=E+G, S=K-J+L, T=L+2H, U=M-E+A-C-G-J+K-F+D-10
You can check your answers for this puzzle on GeoChecker.com.