1.Alan, Bill and Chris dug up 9 nuggets. Their weights were 154, 16, 19, 101, 10, 17, 13, 46 and 22 kgs. They took 3 each. Alan's weighed twice as much as Bill's. How heavy were Chris's nuggets? 
 



2.The product of 3 brothers' ages is 175. Two are twins. How old is the other one? 



3.A man has 2 bankcards, each with a 4 digit number. The 1st number is 4 times the 2nd. The 1st number is the reverse of the 2nd. What is the first number? 



4.Tom has 7 sandwiches, Jan has 5, Simon has none. They share them out equally. Simon leaves, paying for his sandwiches by leaving 12 biscuits. What's the fairest way for Tom and Jan to share out the biscuits? 



5.A cyclist buys a cycle for 15 pounds paying with a 25 pound cheque. The seller changes the cheque next door and gives the cyclist 10 pounds change. The cheque bounces so the seller paid his neighbour back. The cycle cost the seller 11 pounds. How much did the seller lose? 



6.Using four "4"s and common symbols (including the square root, factorial and recurring decimal symbols), make sums whose answers are 0, 1, 2....100 (See Mathematical Bafflers) 
Make fractions using all the digits from 1 to 9 with these values 1/2, 1/3....1/9 
Ans:




7.A greengrocer was selling apples at a penny each, bananas at 2 for a penny and pears at 3 for a penny. A father spent 7p and got the same amount of each type of fruit for each of his 3 children. What did each child get? 




8.A woman bought something costing 34c. She only had 3 coins: $1, 2c and 3c. The shopkeeper had only 2 coins: 25c and 50c. Fortunately another customer had 2 10c coins, a 5c coin, 2 2c coin and a 1c coin. How did they sort things out? 



9.Mr and Mrs A are 120 km apart. A bee is on Mr A's nose. The couple cycle towards each other, Mr A at 25km/h and Mrs A and 15km/h. The bee dashes from Mr A's nose to Mrs A's nose and back again and so on at 60km/h. How far does the bee travel before the cyclists crash? 
 



10.Pick a number. If it's even, divide by 2. If it's odd multiply by 3 and add 1. Continue this until you reach "1". Eg 3-10-5-16-8-4-2-1. Which integer less than 100 produces the longest chain? 




11.Pick a number. Multiply the digits together. Continue until you get a single digit. What is the only 2 digit number which would require more than 3 multiplication? 



12.Starting with 1, place each integer in one of 2 groups so that neither contains a 3 term Arithmetic Progression. How far can you go? 
 



13.The following 2 questions use the following result - "Given integers a and b the biggest number that can't be expressed in the form ia + jb is ab - a - b." 
Apples are packed in boxes of 8 and 15. What is the biggest number of apples that would require loose apples? 




14.A country only has 5p and 7p coins. Make a list of prices that you could give exact money for. What is the highest prices that you couldn't give exact money for? 




15.If D = the day (1-366) in year Y, then the day of the week can be calculated using 
   d = D+Y+(Y-1)/4 - (Y-1)/100 + (Y-1)/400 mod7

where d=1 would mean Sunday, etc. Can the first day of each century (e.g. 1st Jan 2001, 1st Jan 1901) be any day? 




16.Pick 3 digits (not zero) and make 6 2-digit numbers from them. Add up all these numbers, add up all the original digits and divide the first total by the second. 
 



17.How many presents did the "true love" send during the 12 days of Christmas?