The upshot after some more fruitless road searching was we needed to follow the road that looked like a road. There was no road in the place where we couldn't see a road. We agreed the moral of this experience was, if it looks like the main road, it is the main road, no matter where the main road is marked on the map.

After a couple more iterations of road finding, I realised there is a semantic problem looking for 'the' road when there are many roads, all of which may go to the same place via slightly different routes and which may or may not be marked on the map. When we look at a map we point to the line we want to follow and call it 'the' road. As in, "Where is 'the' road we want to cycle on?" We assume this road exists and we assume it is a singular road if there is no other road shown on the map. However, in Mongolia (or in life) 'the' road can be one of many possibilities. Once we focus on 'the' road, we ignore the many other roads which may have advantages we aren't considering.

'The' road approach is a frequent cycle touring problem in cycle touring and not only in Mongolia. It's easy to get focused on a route you are 'supposed' to follow - a line on a map drawn by someone else along which you faithfully track with your brain on autopilot. You follow the little blue dot on your phone screen in a mapping app. The blue dot moves along the road you have downloaded so you can arrive at the 'right' place. But where is the 'right' place? A place someone else has been to, or suggests you go to? Why are you following their path, not your own?

One of the best mishaps in Mongolia was Chris's bike tyre falling apart. Maybe the mishap wasn't the best, but the outcome was great. Chris's tyre deflated rapidly on my birthday. At least the scenery and the weather were good. We tried to find the leak, added more sealant (we ride tubeless) but didn't manage to stop the deflation. Finally, we put a tube in and carried on.

There was more excitement in the day to go – we encountered a river that was hip level (on me) and so turbid we couldn't see the bottom. However, we negotiated it successfully by stripping the bags off the bikes, carrying the gear across, then returning to bring the bikes over one at a time. Post river-crossing, a strong tail wind drove us rapidly towards the town of Gurvanbulag, where we stocked up for my 60th birthday dinner.

In the evening, we had a great three course birthday meal beside the river with German Lars, the first other bikepacker we'd met on our trip. We ate crackers with rehydrated hummus and capsicum, fresh pasta with onion, capsicum and rehydrated veges, yoghurt with banana and apple. We all went to bed knowing our route in the morning would be headed east, up the valley.

In the morning, however, Lars headed east and we limped back to Gurvanbulag because Chris's inner tube was bulging out the side of his tyre. The tyre bead had failed – a first in all our bikepacking. We repaired the tyre using two tyre boots and cloth tape to patch the 10cm long failure, wound electrical tape around the tyre, added a webbing strap, put more tape over the strap to protect it, then added some car tyre from the side of the road fixed on with yet more electrical tape to keep the strap intact. We hung out at the children's playground in Gurvanbulag and used the cell reception (there was rarely reception anywhere out of towns) to call a guesthouse run by an Australian couple who we hoped could help. While the repair was working, we weren't confident Chris could cycle another 200 rough kilometres to the guesthouse where he could access a new tyre.

The upshot was Murray of Fairfield Guesthouse would arrange a tyre to be couriered from Ulan Baatar to Gurvanbulag, but it would take a couple of days. So, what to do for a couple of days? The Gurvanbulag playground was great for a cup of tea but there are only so many antics you can get up to on a yak sculpture.

"Why don't we go to Blue Lake?" I suggested. "A guy in the mini-market asked if I'd been there in a way that suggested it's special to the people here." I'd looked at my map and seen the lake, north of town. We were headed on a road east, not north. I hadn't even considered a detour.

"How far is it?" Chris asked. "I don't know how far long my tyre will last."

I checked our MapOut app. "It's 30km each way. If you get to the lake and then the 10km downhill of the return journey, you can walk back to Gurvanbulag before the tyre arrives."

Chris didn't look thrilled at the possibility of walking 20km pushing his bike but he also wasn't finding the playground riveting. So we headed off to Blue Lake and turned out to be one of our nicest campsites in Mongolia. On the way there we saw children racing horses, practising for Naadam Festival races. The horse riders showed us where to cross the river. I reckon they were very dubious as to whether foreigners would find the right place to cross and, if we did, whether we could cross without getting drowned in the calf-deep water.

We had a beer by the lake - given to us by a Gurvanbulag mini-market owner who felt sorry for us when we returned with our 'broken' tyre. The children from the yurts beside Blue Lake came with their pet goat to give us yoghurt and cheese curd. We swam in the lake and went for a wander around the edge.

Chris's tyre managed the whole 70km return trip without failing, although we stopped every 10km to redo the electrical tape holding the car tyre patch on. We returned to Gurvanbulag well in advance of Chris's new tyre arriving having had a great two-day interlude on 'a' road that we hadn't considered because we were focused on 'the' road. Heres to 'a' roads!