Maths Challenges
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N E P A L M A T H S C H A L L E N G E S
Transport Maths Challenges
MC 1
An electric tempo bus can travel 60kms on one overnight battery charge.
(a) If the average bus route around Kathmandu is 15kms, how many trips can a tempo do in a day?
A tempo needs servicing every 3000kms.
(b) If they are fully used during the day for 7 days of the week, how many weeks are there between each service?
MC 2
A bakery in Namche Bazar has placed this order for supplies from Kathmandu.
15 / 20kg bags of flour @ NPR268 each
5 / 15kg bags of milk powder @ NPR448 each
5 / 5kg bags of raisins @ NPR640 each
2 / 10kg bags of baking powder @ NPR840 each
(a) What is the cost and weight of the supplies?
The goods are flown to Lukla Airport, costing NPR55 per kg
From there porters will carry the items, taking 3 days.
A porter can carry 20kg and costs NPR350 a day.
(b) How many porters will be required?
(c) What is the cost of the porters to carry the supplies?
(d) How much will it cost to fly the supplies to Lukla?
(e) What is the final cost, including transport, to the bakery?
MC 3
A porter uses a 'T' shaped wooden pole to rest their loads on.
Because of the rough ground on the trails, these poles wear down rapidly at a rate of 1mm every 75 rests. Once the poles have worn down 150mm, they will need to be replaced.
If a porter rests on average 15 times a day, how many years will a pole last?
MC 4
A cycist travels 4000kms from Tibet to Everest Base Camp. Because of the rough trails she averages 95 kms between punctures.
Her repair kits hold 10 patches each and only uses 5 patches on each inner tube before replacing it.
How many inner tubes and repair kits did she use?
Nepal People Maths Challenges
MC 1
A Sherpa family near Namche Bazar is going to plant potatoes in an area 6m by 9m. They need to divide the plot into rows 500mm apart with potatoes every 300mm in these rows.
What is the maximum number of potato plants they could plant in their plot?
MC 2
A yak needs 3m x 3m of fresh grass a day or one bale of hay a week. The grass re-grows every 3 weeks in summer, spring and autumn but is unavailable, under snow, in winter for 3 months of the year.
The farmer has one yak and a grass area of 9m x 9m.
How many bales of hay will the farmer need for a year?
MC 3
The average prayer flag is 200mm wide and they are placed 100mm apart on a string. How many flags will you need for a 6m long string?
MC 4
A monk is engraving a prayer, consisting of 7 symbols, on a 150mm diameter prayer wheel.
What is the maximum width of each symbol?
Prove your answer by making a wheel using a strip of paper and draw 7 pictures in the spaces.
(Hint: The circumference of a circle equals 3.14 (pi) times the diameter.)
MC 5
A house contains 1800 stone blocks.
It takes a stone mason 1 hour to shape each block.
(a) How long will it take his team of 10 workers to shape all the blocks?
(b) If they work 12 hour days, 6 days a week, how many weeks will it take?
(c) Porters carry the blocks from a field 5kms away and take 3 hours for a return trip.
If a porter can carry 2 blocks, how long will it take for a team of 6 to complete the task?
(d) How many kms will each porter walk?
(e) If they work 15 hour days, 6 days a week, how many weeks will it take?
Nepal Environment Maths Challenge
Nepal has a land area of 140,797 sq km or 140,797,000,000 sq m and a population of 24 million.
(1) If Nepal was divided up equally for each person how much land would each person get?
(2) If a football field is 100m x 60m, which is bigger?
New Zealand has a land area of 268,021 sq km or 268,021,000,000 sq m and a population of 4 million.
(3) If New Zealand was divided up equally for each person, how much land would each person get?
(4) How many football fields would fit into each persons land.
Climate & Weather Maths Challenge
The monthly maximum and minimum temperature and rainfall in Kathmandu for 2006 is set out below:
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| Max temp | 19 | 20 | 25 | 30 | 30 | 30 | 30 | 29 | 29 | 23 | 23 | 20 |
| Min temp | 2 | 4 | 8 | 11 | 16 | 20 | 21 | 20 | 19 | 15 | 4 | 2 |
| Rainfall | 25 | 25 | 75 | 50 | 100 | 225 | 375 | 360 | 175 | 50 | 10 | 10 |
(1) What was the average max and Min temperature?
(2) What was the average temperature?
(3) Which was the (a) hottest and (b) coldest months in Kathmandu?
(4) What was the total rainfall over the monsoon months of June, July and August?
(5) What percentage of the yearly rainfall fell in the monsoon?
Namche Bazar Maths Challenges
MC 1
You are going to the bakery in Namche Bazar to buy some yummy lunch for your trekking group of 10 people.
Everyone wants a filled roll but only half want a cake.
Filled rolls cost NPR35
Cakes cost NPR10
How much will it cost in Nepal rupees?
MC 2
You are buying some prayer flags to take home.
A string of 30 flags cost NPR300 at one stall, while at another stall you can pick up single flags for NPR5.
Is it cheaper to buy the string of flags?
MC 3
To use the satellite phone at the Everest View Hotel costs NPR140 per minute.
Your call home takes 10 mins.
How much did it cost in US dollars?
(One US dollar equals NPR70)
MC 4
You are staying two nights at the Everest View Hotel.
A standard room costs US$15 per night.
The deluxe oxygen supplied room costs US$20 per night.
Your budget is for US$35.
Which type of room will you choose?
MC 5
There are a number of ways to get to Namche Bazar from Kathmandu.
(a) A 10 hour bus ride to Jiri, then trek for 8 days using a porter to carry your gear and staying in lodges.
The bus to Jiri costs NPR230. Keep a close eye on your luggage as it may disappear mysteriously.
A porter costs NPR 300 a day.
Staying overnight in a typical lodge costs NPR 120 including food.
How much will it cost you to travel to Namche Bazar and stay 2 nights:
(i) In Nepalese rupees?
(ii) In US dollars? (One US dollar equals NPR70)
(b) 
Fly to Lukla, then trek for 2 days using a porter to carry your gear and staying in a lodge for one night.
The flight costs NPR 17450.
Lodges cost NPR 120 per night.
Porters cost NPR 300 a day.
How much will it cost for this trip:
(i) In Nepalese rupees?
(ii) In US dollars? (One US dollar equals NPR70)
(c) You can fly for an hour from Kathmandu directly to Namche Bazar in a helicopter.
It costs US$3000 to hire a helicopter and pilot for this trip.
(i) What are the disadvantages of flying directly to Namche Bazar? (2)
(ii) Which is the cheapest way to get to Namche Bazar?
Kathmandu Maths Challenges
MC 1
On your trip to Base Camp you will need to pick up some last minute gear at the Kathmandu markets.
Some of the prices are in Nepalese rupees and some in American dollars.
One US dollar equals 70 Nepalese rupees.
(a) How much will it cost for all this equipment in US dollars and Nepalese rupees?
Boots US$5.00
Day pack NPR 420
Sleeping bag US$10.00
Drink bottle NPR35
Warm hat US$1.50
Over trousers NPR280
Over Jacket NPR700
Gloves NPR140
Thermal top US$5.00
(b) If one New Zealand dollar equals 50 Nepalese rupees, how much did you spend in New Zealand dollars?
MC 2
You are going on a days sightseeing in Kathmandu.
There are a number forms of transport available.
All charges are in Nepalese rupees (NPR)
A taxi costs a flag fall charge of NPR2 (a charge paid each time you use it) and NPR12 per Km.
A motorised rickshaw costs NPR2 flag fall and NPR6 per km.
A good mountain bike costs NPR400 per day.
How much would it cost in NPR to take 10 sightseeing trips covering 200kms around Kathmandu over three days.
(a) Using a motorised rickshaw?
(b) Using a taxi?
(c) Would it be cheaper to hire a mountain bike?
Nepal Food Maths Challenge
A Sherpa family living near Namche Bazar uses 1kg of potatoes a week. Their family plot of land yields 10 / 25kg bags of potatoes a year.
The family sells any excess potatoes at the Saturday market for NPR85 per kg.
How much money will they make?
E V E R E S T M A T H S C H A L L E N G E S
Facts Maths Challenges
MC 1
If Mt Everest grows in height by 6mm a year how long has it taken to grow to it's present height of 8850m?
MC 2
A child is measuring the height of Mt Everest from the Everest View Hotel, at 3550m above sea level, near Namche Bazar. The hotel is in a direct line of sight with the summit at 8850m.
Using an accurate range finder it has been established that it is 30kms from the summit. There is 5m of level floor to use for the measurement, where a climbing pole stands.
The child sights from the floor to the summit using a 5m string and makes a mark where it intersects the pole.
What is the height from the floor to the mark on the pole? 
Hint: Draw two similar triangles to determine the ratio required.
Sir Edmund Hillary Maths Challenge
Sir Ed is building a classroom at Khumjung School for the Himalayan Trust.
They are using a double skin of plywood for the walls.
For insulation they are using expanded foam sheets in between the layers of plywood.
The plywood sheets are 1.2m x 2.4m.
The building is 7.2m wide x 12m long x 2.4m high. It has windows in both of the long walls 9.6m x 1.2 and a door 1.2 x 2.4 in one short wall.
(a) How many sheets of plywood will be required for the walls?
(b) What is the area of foam insulation required?
Search & Rescue Maths Challenge
A search and rescue radio operator picks up a distress call from an injured climber. The position of the climber is in a northwesterly direction and 70km, as the crow flies, from the search and rescue base.
He dispatches the rescue helicopter. A mountain lies directly in the flight path. The pilot flies north until he is directly east of the injured climber. He then flies straight to the climber, winches them on board and then returns to the base by the same route.
(1) Approx how far did the pilot fly north?
(2) What was the extra distance travelled by the helicopter to skirt around the mountain for the total return flight?
Litter Maths Challenge
(1) Sherpas are paid $13 to bring down an oxygen bottle from the South Col to Base Camp.
An oxygen bottle has a cylinder shape and weighs 2.7kg
The dimensions are: 108mm Diameter x 480mm long.
A Sherpas has a space available in his pack of 350mm x 225mm x 500mm to bring down bottles.
(a) How much money would he earn if he carried down as many bottles as possible?
(b) If his pack already weighed 15kg, what weight did he carry down?
An expedition team requires 10 oxygen bottles per climbing member at a cost of $360 per bottle in Kathmandu.
(c) What is the total cost for bottles for a team of 8 climbers, with sherpas used to return the bottles to base camp?
E V E R E S T B A S E C A M P M A T H S C H A L L E N G E S
Getting There Maths Challenge
An average trekker takes a step covering 700mm or 0.7m. The distance to Base Camp from Namche Bazar along the trails is 110kms. How many steps would an average trekker take?
Measure your own walking step to see how many steps you would take.
At the Camp Maths Challenges
MC 1.
A Sherpa can erect a small tent in 15 mins while a large one takes 30mins. Your expedition has 10 tents. 8 of these are small and the rest are large.
How long will it take your sherpa to erect all the tents?
MC 2.
The size of a four man tent is 2.0m by 2.0m. How much space would 6 men have if they had to squash in, sleeping lying down, in an emergency?
Equipment Maths Challenges
MC 1
If you and a companion had a 50m long rope, how many times would you need to lower (abseil) yourselves down the length of the rope from the summit of Everest to Base Camp?
Everest is 8850m above sea level and Base Camp is 5364m above sea level.
MC 2
You have been caught in an avalanche and buried 9 metres below the surface. You clear the snow away from your mouth and activate your avalanche beacon. Having located the area from the beacon, rescuers are quickly trying to find you. They are using 1.5m extensions on a probing stick.
How many extensions will be needed to find you?
MC 3
On a very hard section of your climb you will need to put in an ice screw every metre to get to the top of a 15m ice cliff.
You only have 14 screws, will you make it?
MC 4
You have one full cylinder of oxygen which contains 1100 litres, and one half full cylinder for your summit push. It is going to take 6 hours there and back. You must leave 2 hours oxygen for an emergency.
What is the maximum rate in litres per minute you can use your oxygen safely?
MC 5.
How much does the total amount of climbers equipment, listed below, weigh in kilograms?
Individual items Weight:
Boots with crampons 1000gms each
Thermals 500gms
Jacket and trousers 1200gms
Fleece Jacket and trousers 1800gms
Outer Jacket and trousers 1500gms
Two sets of gloves 100gms
Hat 150gms
Two pairs of socks 100gms
Harness 100gms
Climbing rope 2000gms
Backpack (loaded) 30000gms
Goggles 15gms
Hardware for fixing ropes 200gms
VHF radio 50gms
Avalanche beacon 15gms
Chocolate bars 70gms
Puttees 100gms
Ice Axe 100gms
MC 6.
(a) On your trek to Camp 1 there are 20 crevasses to cross. You have five ladders available. Two people are needed to secure a ladder and then pick it up again. Your party consists of 6 climbers and 4 Sherpas.
How many times will each pair need to secure a ladder if they take turns?
Hint: You might find it helpful to draw the 20 crevasses in a row
(b) The ladders are numbered 1 to 5.
If you start with no.1, and use them in order, what will the number of the last ladder be?
(c) If it takes 20 mins to correctly secure a ladder and 10 mins to pick it up, how long will it take to get over the crevasses?
Hint: Remember to leave the last 5 ladders in place for the return journey.
MC 7.
A mountaineer is climbing a 10 metre ice cliff, using two ice axes and crampons on each boot.
To start they reach out 2m to get a hold with their ice axes. They step up half a metre with each crampon that has been kicked into the ice. They swing the ice axe with each kick.
How many times will each ice axe be swung to gain a holding point?
MC 8.
Half way up a 10 metre cliff, a climber puts in an ice screw and hooks his safety rope into it. His climbing partner is belaying him from the bottom. (That is holding his safety rope tight.)
What is the maximum distance he can fall?
MC 9.
(a) A climber in the 1920's has a tent with a base of 2m x 1.5m and an overall height of 1.8m. The longer side walls are vertical for 300mm then pitch up to a central ridge.
(b) A modern tent resembles a half cylinder on a 300mm high vertical base. The base of the tent is 1.5m and the length 2.5m.
(1) What is the volume of each tent?
To avoid the toxic fumes given off from cooking in the tents, ventilation holes must be provided. These are placed at the top of the tent to release carbon monoxide and at the bottom to allow oxygen in. These must be a minimum of 5000 sq mms per 1 cubic metre of volume of the tent.
(2) What size holes will be necessary for each tent if one of the dimensions is 150mm?
Hints: The volume of a regular prism shape is the area of the end times it's length. The area of a semi circle equals 1/2 Pi (r x r), where r is the radius of the circle.
Base Camp Food Maths Challenge
A climber is packing her kit for her summit attempt.
She will need 2 litres of water a day and 3 litres at night for cooking and drinking. Apart from the first day she will melt snow to obtain the water.
Her plan is to spend 5 nights on the mountain but needs to allow for possible delays with storms and possible rescues.
The gas cooker she is using takes 5mins to boil a litre of water.
One cylinder of gas lasts 30mins.
If she took 6 cans of gas how many extra days for storms has she allowed for?
M A C H I N E M A T H S C H A L L E N G E S
Production Maths Challenges
'Infusion moulding of a helicopter body part'.
MC 1.
Carbon fibre comes in rolls 1200 wide by 15 m.
The helicopter tail boom half mould is 5m long by 1m wide.
How many rolls will you need to make 3 complete tail booms?
MC 2.
One litre (1000mls) of resin covers approx 3sqm.
If your mould is 4.5sqm how much working resin will you need to mix?
MC 3.
A liquid resin and hardener are mixed together to produce a working resin that sets in approx 4hours.
The resin and hardener is mixed in the ratio of 4 to 1.
This means that 800mls of resin is mixed with 200mls of hardener to make up one litre of working resin.
What quantity of hardener will you need, to make up
5 litres of working resin?
F U N D S M A T H S C H A L L E N G E S
Organisations Maths Challenges
MC 1
As part of the organizing committee you need to work out some costs for an expedition.
Your group consists of 5 climbers and 5 support staff with 5000kg of gear.
The airfare from Auckland to Bangkok is $1575 per person, and from Bangkok to Kathmandu is $225 per person.
Freight costs from Auckland to Kathmandu is $2500 per 1000kg
Hotel accommodation is $50 a night per person.
The flight from Kathmandu to Lukla is $250 per person.
Freight from Kathmandu to Lukla costs $4000 per 1000kg.
How much is it going to cost to get the expedition to Lukla if the group needs to stay 2 nights in Kathmandu?
MC 2.
'Yakidy yak'
A yak can carry 125kg.
(a) How many will be needed to carry the 5000kg of gear to Base Camp?
One yak herder is needed for every 20 yaks.
Use your answer from (a) for the number of yaks in this next question.
A yak herder costs $5.00 per day and a yak costs $10.00 per day.
(b) How much will it cost to travel the 12 days to Base Camp?
MC 3.
'Yaks on the bridge'
On a trek towards Base Camp there are 6 bridges.
On an average, only 3 yaks can safely be on a bridge at a time.
It takes 10mins longer for three yaks to cross a bridge than it does on the normal trail.
How much longer will it take for 39 yaks to complete the trail?
MC 4.
Yaks travel on average 20 to 30 kms a day.
What would be the quickest time and the longest time taken From Lukla to Base Camp if it is 120 kms?
M A T H S C HA L L E N G E S A N S W E R S
N e p a l A n s w e r s
People
MC 1: 360 plants
MC 2: 36 bales
MC 3: 20 flags
MC 4: 67mm
MC 5:
(a) 180hrs
(b) 2 ½ weeks
(c) 450hrs
(d) 1500kms
(e) 5 weeks
Transport
MC 1:
(a) 4 trips
(b) 7 weeks
MC 2:
(a) NPR11140, 420kg
(b) 21
(c) NPR22050
(d) NPR23100
(e) NPR56290
MC 3: 2 years
MC 4: 7 inner tubes, 4 repair kits
Environment
(1) 5866.5 sq m
(2) Football field
(3) 67005 sq m
(4) 11 football fields
Climate & Weather
(1) max 25.66, min 11.83
(2) 18.74
(3) (a) July (b) January
(4) 960mm
(5) 960/1480 x 100 = 65%
Kathmandu
MC 1:
(a) US$44.00, NPR3080
(b) 3080 x 50 or 44 x 70/50 equals NZ$61.60
MC 2:
(a) 1220
(b) 2420
(c) Yes
Food
250 – 52 = 198 x 85 = NPR16830
Namche Bazar
MC 1: NPR 400
MC 2: No
MC 3: US$20
MC 4: Standard room
MC 5:(a) 230 + 8 x 300 + 9 x 120 = (i) NPR3710 = (ii) US$52
(b) 17450 + 3 x 120 +2 x 300 = (i) NPR18410 = (ii) US$263)
(c) (i) You do not get acclimatised, The trip is very expensive
(ii) (a)
E v e r e s t A n s w e r s
Facts
MC 1:
1,475,000 years
MC 2:
C/A =D/B, C = 5D/B, C = 5 x 5300 / 30000 = 883mm
Sir Edmund Hillary
(a) 2 x 6 + 2 x 10 =32 x 2 = 64 sheets, less windows and doors –18 = 46 sheets
(b) 2.4 x 12 x 2 + 2.4 x 7.2 x 2 = 92.16 sqm, less windows and door – 9 x 1.2 x 2.4 = - 25.92 = 66.24 sqm. Or 23 sheets x 1.2 x 2.4 = 66.24 sqm
Search & Rescue
(1) 50km, (2) 60km
Litter
(a) 6 x 13 = $78
(b) 6 x 2.7 = 16.2 + 15 = 31.2kg
(c) 10 x 360 = 3600 x 8 = 28800 + (80 x 13) = $29840
E v e r e s t B a s e C a m p A n s w e r s
Getting There
110 x 1000 = 110000m / 0.7 = 157,143 steps
At the Camp
MC 1: 8 x 15 = 120 + (2 x 30 = 60) = 180mins or 3hours
MC 2: 2000 / 6 = 333mm x 2.0
Equipment
MC 1: 8850 – 5364 = 3486 / 50 = 70 times
MC 2: 9/1.5 = 6
MC 3: Yes
MC 4: 1100 + 550 =1650 / (8 x 60 = 480) = 3litres/min
MC 5: Total 39000gms = 39kg
MC 6:
(a) 4
(b) 5
(c) 550mins or 9hrs 10mins
MC 7: 9 times
MC 8: 5m
MC 9.
(1) (a) 3.15 cubic metres, (b) 3.33 cubic metres
(2) (a) 15750/150 = 105mm x 150mm (b) 16650/150 = 111mm x 150mm
Base Camp Food
6 x 30 =180 mins/25 = 7.2 days = 2 days extra for storms
M a c h i n e A n s w e r s
Production
MC 1: 2 rolls
MC 2: 1500mls
MC 3: 1000mls
F u n d s A n s w e r s
Organisations
MC 1:
Air Fares 1575 + 225 + 250 = 2050 x 10 = $20,500
Freight costs 4000 + 2500 = 6500 x 5 = $32500
Accommodation 50 x 2 x 10 = $1000
1000 + 32500 + 20500 = $54000
MC 2:
(a) 1500 / 125 = 40
(b) Yaks: 40 x $10 = 400 x 12 = $4800
Herders: 2 x $5 = 10 x 12 = $120
4800 + 120 = $4920
MC 3:
39 /3 = 13 x 10 =130 x 6 = 780 / 60 = 13 hours
MC 4:
Max 120 / 20 = 6 days
Min 120 / 30 = 4 days
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